tag:blogger.com,1999:blog-78625872887014184942024-02-08T03:28:00.821-08:00Strengthening mathematical knowledgeFariel Mohan created a virtual classroom to strngthen the mathematical knowledge of the students by providng a platform for collaborationFariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.comBlogger66125tag:blogger.com,1999:blog-7862587288701418494.post-11739967298388790462009-05-04T13:39:00.000-07:002009-05-04T13:47:43.501-07:00Missing NamesThere are no real names for the blog names listed below. If your blog name is on the list, please email your real name, blog name and Student ID<span class="Apple-style-span" style="font-weight: bold;"> IMMEDIATELY</span> to fariel.mohan (at) utt.edu.tt<div><br /></div><div>These are very important to your grades. Please pass the message along to your classmates</div><div><br /></div><div> @ce</div><div>110000296</div><div>~*DJ HalfTime*~</div><div>Aki</div><div>asriel10star</div><div>Bailey</div><div>Born to Perform</div><div>braniac</div><div>Colour me orange again</div><div>cfc</div><div>ChckPrpl</div><div>damon</div><div>dutchess</div><div>empress</div><div>FLASH</div><div>Goldfinger</div><div>HEAVY T BUMPER</div><div>jade</div><div>Joh</div><div>kingsulton</div><div>Kurosaki Ichigo</div><div>Lykke</div><div>mathwiz69</div><div>maths hate or love it</div><div>phantom</div><div>Q45</div><div>Quantum100</div><div>renjisan</div><div>ridiclyric</div><div>saeed</div><div>small man</div><div>SMILEY</div><div>starflake</div><div>Suspect R</div><div>tapolin</div><div>The best one</div><div>toffee</div><div>turbo</div><div>VNKOrpgujvj3sWdl6kEdABecHIX4</div><div>Weezy</div><div>zipper<br /></div><div><br />Again, if your name appears on the list, please email your real name, blog name and Student ID<span class="Apple-style-span" style="font-weight: bold; "> IMMEDIATELY</span> to fariel.mohan (at) utt.edu.tt</div>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com1tag:blogger.com,1999:blog-7862587288701418494.post-49567497538213156542009-04-27T19:50:00.001-07:002009-04-27T19:57:54.988-07:00Integration errorswhen you integrate 4x^5 + 3<br />you get 4x^6/6 +<span style="font-size:180%;"> <strong>3x + c</strong></span><br /><strong><span style="font-size:180%;"></span></strong><br />when you integrate 2<br />you get<span style="font-size:180%;"> <strong>2x + c</strong></span><br /><strong><span style="font-size:180%;"></span></strong><br /><strong><span style="font-size:180%;">Exams is on calculus and matrix only</span></strong><br /><strong><span style="font-size:180%;"></span></strong><br /><strong><span style="font-size:180%;">calculus</span></strong><br /><strong><span style="font-size:180%;">differentiation is gradient machine</span></strong><br /><strong><span style="font-size:180%;">give a point and you will get the gradient from gradient machine</span></strong><br /><strong><span style="font-size:180%;">differentiate polynomial, sin x, cos x, e^x , ln x </span></strong><br /><strong><span style="font-size:180%;">real life application RATE OF CHANGE is differentiation</span></strong><br /><strong><span style="font-size:180%;">VELOCITY = change in distance/ time</span></strong><br /><strong><span style="font-size:180%;">ACCELERATION = change in velocity /time</span></strong><br /><strong><span style="font-size:180%;"></span></strong><br /><strong><span style="font-size:180%;">Integration</span></strong><br /><strong><span style="font-size:180%;">polynomial</span></strong><br /><strong><span style="font-size:180%;">sin x</span></strong><br /><strong><span style="font-size:180%;">cos x</span></strong><br /><strong><span style="font-size:180%;">area under curve</span></strong><br /><strong><span style="font-size:180%;">definite integral means point given so you can find the value of c</span></strong><br /><strong><span style="font-size:180%;"></span></strong><br /><strong><span style="font-size:180%;">GOOD LUCK</span></strong>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com2tag:blogger.com,1999:blog-7862587288701418494.post-80370791372932641732009-04-23T08:40:00.000-07:002009-04-23T08:42:46.604-07:00Integration QuestiosIntegrate the following<br /><br />1. dy/dx = 5x^3 + 2x^2 + 5<br /><br />2. dy/dx = 6x + 1<br /><br />3. dy/dx = 2<br /><br />4. dy/dx = 8x^5 - 5x^3 + 4x<br /><br />5. dy/dx = 7x^2 + 3x + 4Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com13tag:blogger.com,1999:blog-7862587288701418494.post-45971063733918820152009-04-19T09:51:00.000-07:002009-04-22T14:31:00.843-07:00A particle moves in a straight line and at point P, it's velocity is given as v = 7t^2 - 5t +3. The particle comes to rest at point Q.<br /><br />1. What is the acceleration at Q if it arrives at Q when t=7?<br />2. How far does the particle travel in t=1 to t=4?Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com6tag:blogger.com,1999:blog-7862587288701418494.post-1659277529408690152009-04-21T19:22:00.000-07:002009-04-21T19:31:55.128-07:00Integration +c being forgottenToo many forgetting the + c in integration<br /><br />question2<br />dy/dx=2x(x-3)<br />dy/dx=2x^2-6x<br />y=2/3x^3-3x^2<br /><br />What about the + c<br />y=2/3x^3-3x^2 + c<br /><br />To find the value of c use the point provided (3,6) x = 3 and y = 6<br />so c can be found<br /><br /><strong>What about a question with v= and distance is required integrate yes but do not forget the +c</strong><br /><strong></strong><br />b)TO find the total distance travelled u need to integrate the (V) velocity.<br />v = 5t -3t^2 + 2<br />s= 5/2t^2 - t^3 + 2t<br /><br />it must be<br />s= 5/2t^2 - t^3 + 2t + cFariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com2tag:blogger.com,1999:blog-7862587288701418494.post-18991025130900477632009-04-20T18:31:00.000-07:002009-04-20T18:39:10.990-07:00Errors1. y = 6x^3 + 4x^2 -5x<br />when you differentiate how can the y remain y<br />dy/dx = 18x^2 + 8x -5<br /><br />2. y^2 = x^3 + 16 is in the syllabus differentiating with 2 unknowns<br />some of you missed this class<br /><br />differentiate term by term as normal and if the current term is a y term differentiate w.r.t y and then multiply by dy/dx<br /><br />2y dy/dx = 3x^2<br /><br />3. 1/y = 4x + 4<br />no downstairs<br />y^-1 = 4x + 4<br />differentiate term by term<br /><br />-y^-2 dy/dx = 4Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com0tag:blogger.com,1999:blog-7862587288701418494.post-53684133116861724802009-04-19T18:59:00.000-07:002009-04-19T19:05:09.782-07:00Common errors being made<ol><li>y = 2x + <span style="font-size:85%;">8/x^<span style="font-family:times new roman;">2</span><span style="font-family:arial;"> <span style="font-size:130%;">find dy/dx no downstairs y = 2x + 8x^-2 BUT when differentiating dy/dx = 2 -16x^-3 NOTE -2 -1 = -3</span></span></span></li><li><span style="font-family:Arial;font-size:130%;">y = ln (2x + 3) use sub for m BUT dy/dm CANNOT be the same as dy/dm instead dy/dx must be= dy/dm * dm/dx</span></li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com0tag:blogger.com,1999:blog-7862587288701418494.post-63868256646322923802009-04-17T18:40:00.000-07:002009-04-19T09:15:46.085-07:00Project (20%)These are all the projects I received except for Brent and Azad (no ID on project but marked)<br /><br />107000184<br />20<br />108002539<br />20<br />109000055<br />20<br />109000336<br />20<br />109003667<br />20<br />109003729<br />20<br />109004010<br />20<br />109004027<br />20<br />110000051<br />20<br />110000060<br />20<br />110000080<br />20<br />110000117<br />20<br />110000164<br />20<br />110000179<br />20<br />110000215<br />20<br />110000226<br />20<br />110000228<br />20<br />110000239<br />20<br />110000243<br />20<br />110000283<br />20<br />110000284<br />20<br />110000303<br />20<br />110000314<br />20<br />110000316<br />20<br /><br />109004186<br />19<br />110000129<br />19<br />110000139<br />19<br />110000234<br />19<br />110000250<br />19<br />109000083<br />18<br />109002131<br />18<br />109002140<br />18<br />109002469<br />18<br />109004071<br />18<br />110000235<br />18<br />110000241<br />18<br />110000250<br />18<br />110000266<br />18<br />110000288<br />18<br />110000300<br />18<br />110000328<br />18<br />109002069<br />17<br />109002277<br />17<br />110000320<br />17<br />100000026<br />16<br />110000162<br />16<br />110000223<br />16<br />110000286<br />16<br /><br />109000323<br />15<br />109002393<br />15<br />109004801<br />15<br />109004820<br />15<br />110000111<br />15<br />110000229<br />15<br />110000257<br />15<br />110000264<br />15<br />110000265<br />15<br />110000280<br />15<br />110000282<br />15<br />110000319<br />15<br />110000294<br />14<br />110000304<br />14<br />109002449<br />13<br />110000259<br />13<br />110000271<br />13<br />110000197<br />12<br />110000112<br />10<br /><br />110000236<br />8<br />110000254<br />7<br />110000067<br />5<br />110000102<br />5<br />110000219<br />5<br />109003257<br />14<br />110000022<br />20<br />110000304<br />4<br />109002035<br />20Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com2tag:blogger.com,1999:blog-7862587288701418494.post-46056928677580344712009-04-12T18:49:00.000-07:002009-04-12T18:57:43.346-07:00Revision<ol><li>Find the trap area from (1,4) to (2,1) and the line y = 7 - 3x and the curve y = 4/x^2</li><li>Find the equation of the curve which passes through the point (3,6) and for which dy/dx = 2x(x -3). Hint open brackets first then integrate.</li><li>Differentiate e^(3-2x)</li><li>A particle moves in a straight line so that, t seconds after passing through a fixed point O, its velocity, is giveb by v = 5t -3t^2 + 2. The particle comes to instantaneous rest at the point Q. Find</li></ol><p>a) the acceleration of the particle atQ</p><p>b) the total distance travelled in the time interval t = 0 to t =3.</p>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com13tag:blogger.com,1999:blog-7862587288701418494.post-35262901399037810472009-04-12T18:04:00.000-07:002009-04-12T18:12:25.438-07:00VelocityA particle moves in a straight line so that at time t seconds after passing through a fixed point, its velocity, v m/s, is given by v = 6 cos 2t. Find<br /><ol><li>the two smallest positive values of t for which the particle is at instanteneous rest</li><li>the distance between the positions of instantaneous rest corresponding to these two values of t</li><li>the greatest magnitude of the accelerstion</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com6tag:blogger.com,1999:blog-7862587288701418494.post-13656373604932160872009-04-10T09:32:00.000-07:002009-04-10T09:38:16.325-07:00Find dy/dx1. y = 6x^3 + 4x^2 - 5x<br /><br />2. y^2 = x^3 + 16<br /><br />3. 1/y = 4x + 4<br /><br />4. y = 3x^4 + 3(x^2 + 5)<br /><br />5. y + 6 = 4x + 9y - 3x^2Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com41tag:blogger.com,1999:blog-7862587288701418494.post-78762887439053162202009-04-08T19:17:00.000-07:002009-04-08T19:32:08.758-07:00Questions 2<ol><li>A curve has equation y = 4/(2)^.5, find dy/dx</li><li>A curve is such that dy/dx = 16/x^3 and (1,4) is a point on the curve, find the equation of the curve.</li><li>y = 6theta - sin 2 theta, find dy/dx</li><li></li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com22tag:blogger.com,1999:blog-7862587288701418494.post-11531538483413148182009-04-08T19:09:00.000-07:002009-04-08T19:17:12.834-07:00Questions 1<ol><li>The equation of a curve is y = 2x + 8/x^2</li></ol><p>find dy/dx and d^2ydx^2</p><ol><li>Differentiate ln (2x + 3)</li><li>A curve is such that dy/dx = 2x^2 -5. Given that the point (3,8) lies on the curve, find the equation of the curve.</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com23tag:blogger.com,1999:blog-7862587288701418494.post-59346247577505345912009-04-07T18:21:00.000-07:002009-04-07T18:28:55.670-07:00Matrices<ol><li>....... is used to represent space in the matrix</li></ol><p>14 ................6</p><p>5x-3 ............8</p><p>What value of x will this matrix be singular?</p><ol><li>What values of p will make this matrix singular</li></ol><p>6p + 2 .........8</p><p>5 ...................3p</p><p></p><ol><li>Can a singular matrix have an inverse, justify your answer?</li><li>Tom bought 6 plums and 5 mangoes for $40. Jane bought 3 similar plums and 4 similar mangoes for $23. Using the matrix method determine the price of 1 plum and the price of 1 mango.</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com25tag:blogger.com,1999:blog-7862587288701418494.post-65294698164423819882009-04-07T02:33:00.000-07:002009-04-07T02:34:46.370-07:00Find the product of the following matriciesFind the product of the following matricies<br /><br />1.<br />| 1 5 | | 2 2 |<br />| 3 8 | . | 4 5 |<br /><br />2.<br />| 5 9 | | 2 1 |<br />| 3 2 | . | 2 7 |<br /><br />3.<br />| 4 1 | | 1 2 |<br />| 0 2 | . | 4 1 |<br /><br />4.<br />| 9 7 | | 3 3 |<br />| 9 8 | . | 3 3 |<br /><br />5.<br />| 4 4 | | 5 2 |<br />| 4 4 | . | 3 5 |<br /><br />6.<br />| 1 0 | | 0 5 |<br />| 0 8 | . | 4 4 |<br /><br />7.<br />| 2 3 | | 3 2 |<br />| 3 6 | . | 3 5 |<br /><br />8.<br />| 0 5 | | 0 0 |<br />| 0 8 | . | 4 5 |<br /><br />9.<br />| 2 2 | | 3 3 |<br />| 2 2 | . | 3 3 |<br /><br />10.<br />| 3 6 | | 6 3 |<br />| 6 3 | . | 3 6 |Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com63tag:blogger.com,1999:blog-7862587288701418494.post-88886460291447971162009-03-26T20:53:00.000-07:002009-03-26T21:29:08.475-07:00diff questions<ol><li>The displacement s of a piston during each 8-s is given by s = 8t -t^2. For what value of t is the velocity of the piston 4?</li><li>The distance s travelled by a subway train after the brakes are applied is given by s = 20t -2t^2 How far does it travel after the brakes are applied in coming to a stop?</li><li>Water is being drained from a pond such that the volume V of water in the pond after t hours is given by V = 50(60-t)^2. Find the rate at which the pond is being drained after 4 hours.</li><li>The electric field E at a distance r from a point charge is E=k/r^2 where k is a constant. Find an expression for the instantaneous rate of change of the electric field with respect to r.</li><li>The voltage V induced in an inductor in an electric circuit is given by V = L(d^2q/dt^2) where L is the inductance. Find the expression for the voltge induced in a 1.6 H inductor if q = (2t + 1)^.5 -1.</li><li>The altitude h of a certain rocket as a function of the time t after launching is given by h = 550t - 4.9 t^2. What is the maximum altitude the rocket attains?</li><li>The blade of a saber saw moves vertically up and down and its displacement is given by y = 1.85 sin 36∏t. Find the velocity of the blade for t=0.025.</li><li>The charge q on a capacitor in a circuit containing a capacitor of capacitance C, a resistance R, and a source of voltage Eis given by q = CE(1 - e^(-t/RC) ). Show that this equation satisfies the equation Rdq/dt + q/C = E.</li><li>An earth orbiting satellite is launched such that its altitude is given by y = 240(1 - e^(-.05t)). Find the velocity of the satellite for t= 10.</li><li>Differentiate y = 7sin x + ln (4x^2 +1)</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com57tag:blogger.com,1999:blog-7862587288701418494.post-18883426988337337402009-03-25T20:13:00.000-07:002009-03-25T20:24:01.308-07:00Function Diff<ol><li>Differentiate m = 8/e^t - e^t</li><li>Differentiate v = 7 cos 3a + 8a^5. What is dv/da when a = 1/2 ∏</li><li>∫5sinb db </li><li><br />∫5cosm dm</li><li><br />∫5sinb + 9b^4 db </li><li><br />∫5/x dx</li><li><br />∫5e^x dx </li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com24tag:blogger.com,1999:blog-7862587288701418494.post-7758475867796198472009-03-22T09:14:00.001-07:002009-03-22T09:14:31.803-07:00Question Set 8 (Logs)Solve the Following:<br /><br />2 = 1.4^x<br /><br />15 = 6.1^x-1<br /><br />6 = 10^x+1<br /><br />14^x = 6^x<br /><br />4 = 3.3^x<br /><br />18 = 3.1^x<br /><br /><br /><br />Find b in the following:<br /><br />log[4]16 = b<br /><br />log[3]81 = b<br /><br />log[2]16 = b<br /><br />log[5]125 = b<br /><br />log[3]9 = b<br /><br />log[6]216 = b<br /><br />log[8]64 = b<br /><br />log[4]64 = b<br /><br />log[b]625 = 4<br /><br />log[b]49 = 2<br /><br />log[b]27 = 3<br /><br />log[b]81 = 2<br /><br />log[b]4 = 2<br /><br />log[b]16 = 4<br /><br />log[3]b = 6<br /><br />log[4]b = 3<br /><br />log[5]b = 3125<br /><br />log[10]b = 1<br /><br />log[9]b = 4<br /><br />log[2]b = 6<br /><br />log[3]b = 4<br /><br />log[8]b = 3Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com85tag:blogger.com,1999:blog-7862587288701418494.post-43700098384076907932009-03-21T17:05:00.000-07:002009-03-21T19:03:44.974-07:00Question set 7<ol><li>Let A be the area of a circle with radius r at time t. If the radius changes at a rate of 2 in/sec, at what rate is the circle's area changing when r = 1?</li><li>Let A be the area of a square with side s at time t. If the side changes at a rate of -4 mm/week, at what rate is the square's area changing when s = 3?</li><li>Let V be the volume of a sphere with radius r at time t. If the radius changes at a rate of 3 ft/min, at what rate is the sphere's volume changing when r = 2?</li><li>Let S be the surface area of a sphere with radius r at time t. If the radius changes at a rate of -5 m/hr, at what rate is the sphere's surface area changing when r = 1?</li><li>Let V be the volume of a cube with side s at time t. If the side changes at a rate of 10 in/hr, at what rate is the cube's volume changing when s = 5?</li><li>Let S be the surface area of a cube with side s at time t. If the side changes at a rate of 7 cm/sec, at what rate is the cube's surface area changing when s = 3?</li><li>Let A be the area of a circle with radius r at time t. If the radius changes at a rate of -3 ft/sec, at what rate is the circle's area changing when r = 5?</li><li>Let A be the area of a square with side s at time t. If the side changes at a rate of 2 m/day, at what rate is the square's area changing when s = 10?</li><li>Let V be the volume of a sphere with radius r at time t. If the radius changes at a rate of -8 in/min, at what rate is the sphere's volume changing when r = 7?</li><li></li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com26tag:blogger.com,1999:blog-7862587288701418494.post-87647033629523082442009-03-21T16:57:00.000-07:002009-03-21T17:04:25.585-07:00Question set 6<ol><li>An object is thrown in the air from an initial height of 12 feet, with an initial upward velocity of 16 feet/second?<br />How long will the object be in the air?<br />What will the velocity of the object be after 1 second? </li><li>An object is thrown in the air from an initial height of 48 feet, with an initial upward velocity of 32 feet/second?<br />How long will the object be in the air?<br />What will the velocity of the object be after 2 seconds? </li><li>An object is thrown in the air from an initial height of 100 feet, with an initial upward velocity of 10 feet/second?<br />How long will the object be in the air?<br />What will the velocity of the object be after 2 seconds? </li><li>An object is thrown in the air from an initial height of 400 feet, with an initial upward velocity of 50 feet/second?<br />How long will the object be in the air?<br />What will the velocity of the object be after 4 seconds? </li><li>An object is thrown in the air from an initial height of 75 feet, with an initial upward velocity of 200 feet/second?<br />How long will the object be in the air?<br />What will the velocity of the object be after 5 seconds? </li><li>Suppose it costs -x^2 + 400x dollars to produce x computers/day. Compute the marginal cost to estimate the cost of producing one more computer each day, if current production is 100 computers/day. </li><li>If the position of an object at time t is given by the function<br />s(t) = 3t + 2 meters what are the velocity and acceleration when t = 3 seconds?</li><li>If the position of an object at time t is given by the function<br />s(t) = t3 - t meters what are the velocity and acceleration when t = 5 seconds?</li><li>If the position of an object at time t is given by the function<br />s(t) = 3t3 - 10t2 meters what are the velocity and acceleration when t = 2 seconds?</li><li>If the position of an object at time t is given by the function<br />s(t) = sin t meters what are the velocity and acceleration when t = pi/4 seconds?</li><li> If the position of an object at time t is given by the function<br />s(t) = cos 2t meters what are the velocity and acceleration when t = pi/4 seconds?</li><li>If the position of an object at time t is given by the function<br />s(t) = sin t + t meters what are the velocity and acceleration when t = pi/2 seconds?</li><li> If the position of an object at time t is given by the function<br />s(t) = cos t + sin t meters what are the velocity and acceleration when t = pi seconds?</li><li>If the position of an object at time t is given by the function<br />s(t) = (1/2)t3 + 2t meters what are the velocity and acceleration when t = 1 second?</li><li>If the position of an object at time t is given by the function<br />s(t) = 6t2 - 8t + 19 meters what are the velocity and acceleration when t = 4 seconds?</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com12tag:blogger.com,1999:blog-7862587288701418494.post-5556704064359826962009-03-21T16:49:00.000-07:002009-03-21T16:57:05.957-07:00Question set 5<ol><li>Let f(x) = sin x. Find the first 3 derivatives of f.</li><li>Let f(t) = 5 cos t. Find the first 4 derivatives of f.</li><li>Let f(x) = 3cos x + 5x. Find the first 3 derivatives of f.</li><li>Let f(t) = 2t + sin t. Find the first 3 derivatives of f.</li><li>Let f(t) = 1/t2 - sin t. Find the first 2 derivatives of f.</li><li>Let f(x) = sin x - cos x. Find the first 4 derivatives of f.</li><li>Let f(x) = 2sin x + 3cos x. Find the first 4 derivatives of f.</li><li>Let f(x) = 4sin x + 1/x. Find the first 3 derivatives of f.</li><li>Let f(t) = -3sin t + 1/2 cos t. Find the first 3 derivatives of f.</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com7tag:blogger.com,1999:blog-7862587288701418494.post-23542363529604592092009-03-21T16:15:00.000-07:002009-03-21T16:19:22.935-07:00Question set 4<ol><li>y = e ^(2x). Find dy/dx and d^2y/dx^2</li><li>y = sin x . Find d^133 y /d x^133</li><li></li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com6tag:blogger.com,1999:blog-7862587288701418494.post-86656591674541650422009-03-21T15:55:00.000-07:002009-03-21T16:07:15.232-07:00Question set 3<ol><li>A stone is dropped into a pond, the ripples forming concentric circles which expand. At what rate is the area of one of these circles increasing when the radius is 4 m and increasing at the rate of 0.5 ms-1?</li><li>The tuning frequency f of an electronic tuner is inversely proportional to the square root of the capacitance C in the circuit.<br />If f = 920 kHz for C = 3.5 pF, find how fast f is changing at this frequency if dC/dt = 0.3 pF/s.</li><li>An object falling from rest has displacement s in cm given by s = 490t2, where t is in seconds.<br />What is the velocity when t = 10 s?</li><li>Find the equation of the tangent to the curve y = 3x − x^3 at x = 2.</li><li>Find the derivative of the function<br />y = x^<span style="font-size:85%;">1/4</span> - <span style="font-size:130%;">2/x</span></li><li>Find dy/dx for y = (5x + 7)^12. </li><li>Find dy/dx for y = (x^2+ 3)^5.</li><li>Find if dy/dx y = √(4x^2 -x). </li><li>Find dy/dx if y = (2x^3 - 1)^4</li><li>Find dy/dx if y =(4x^5 - 1/(7 x^ 3))^4<br /></li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com22tag:blogger.com,1999:blog-7862587288701418494.post-23878620305324163332009-03-21T15:42:00.000-07:002009-03-21T15:53:32.535-07:00Question set 2<ol><li><br />You fire a cannonball upward so that its distance (in feet) above the ground<br />t seconds after firing is given by h(t) = −16t^2 + 144t. Find the maximum height (dh/dt = 0) it reaches and the number of seconds it takes to reach that height.</li><li>The daily profit, P, of an oil refinery is given by<br />P = 8x − 0.02x^2,<br />where x is the number of barrels of oil refined. How many barrels will give maximum profit (dP/dx = 0) and what is the maximum profit?</li><li>A rectangular storage area is to be constructed along the side of a tall building. A security fence is required along the remaining 3 sides of the area. What is the maximum area that can be enclosed with 800 m of fencing?</li><li>A box with a square base has no top. If 64 cm2 of material is used, what is the maximum possible volume for the box?</li></ol>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com15tag:blogger.com,1999:blog-7862587288701418494.post-71702651916746729882009-03-21T14:09:00.000-07:002009-03-21T15:26:39.219-07:00Questions cosθ sin θ sinθ - cosθ<ul><li>Solve x = log[3] 81 + log[3]1/9</li></ul><p>For what value of x, the following matrix is singular ?<br />(5-x) (x + 1) </p><p>(2) ( 4)</p><p>3.. The matrix A = </p><p>3 2 satisfies the relation A2 - 4A + I = 0. Find A-1.<br />1 1 </p><p>4. cosθ sin θ sinθ - cosθ<br />Simpliy cosθ + sinθ<br />- sinθ cosθ cosθ sinθ</p><p>5. Evaluate</p><p>-1<br />∫ 1/x dx<u><br /></u>-4 </p><p></p><p>6. A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?</p><p>7. A window is in the form of a rectangle surmounted by a semi-circular opening.<br />The total perimeter of the window is 10m. Find the dimensions of the window to<br />admit maximum light through the whole opening</p><p> </p><p>8. A square piece of tin of side 48 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off, so that the volume of the box is the maximum possible? Also find the maximum volume.</p>Fariel Mohanhttp://www.blogger.com/profile/13632502379336399563noreply@blogger.com11