- 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?
- The tuning frequency f of an electronic tuner is inversely proportional to the square root of the capacitance C in the circuit.
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. - An object falling from rest has displacement s in cm given by s = 490t2, where t is in seconds.
What is the velocity when t = 10 s? - Find the equation of the tangent to the curve y = 3x − x^3 at x = 2.
- Find the derivative of the function
y = x^1/4 - 2/x - Find dy/dx for y = (5x + 7)^12.
- Find dy/dx for y = (x^2+ 3)^5.
- Find if dy/dx y = √(4x^2 -x).
- Find dy/dx if y = (2x^3 - 1)^4
- Find dy/dx if y =(4x^5 - 1/(7 x^ 3))^4
Saturday, March 21, 2009
Question set 3
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Question 2
ReplyDeletes= 490t^2
velocity = displacement/time
ds/dt = (490*2) t
= 980 t
if t=10s
then ds/dt = 980 (10)
= 9800 cm/s
= 98 m/s
or
displacement = ds/dt * time
= 9800 *10
= 98 000cm
= 980 m
velocity = displacement/ time
= 980/10
= 98 m/s
no 6
ReplyDeletey = (5x + 7)^12
let m = 5x +7
dm/dx = 5
y = m^12
dy/dm = 12m^11
dy/dx = dm/dx * dy/dm
= 5 * 12(5x+7)^11
no 7
ReplyDeletelet m = x^2 + 3
dm/dx = 2x
y = m^5
dy/dm = 5m^4
dy/dx = dm/dx * dy/dm
= 2x * 5(x^2 + 3)^4
no 8
ReplyDeletey = (4x^2 - x)^1/2
let m = 4x^2 - x
dm/dx = 8x - 1
y = m^1/2
dy/dm = 1/2m^-1/2
dy/dx = dm/dx * dy/dm
= (8x-1) * 1/2(4x^2 - x)^-1/2
no 9
ReplyDeletelet m = 2x^3 - 1
dm/dx = 6x^2
y = m^4
dy/dm = 4m^3
dy/dx = dm/dx * dy/dm
= 6x^2 * 4(2x^3-1)^3
no 10
ReplyDeletelet m = (4x^5 - 1)/(7x^3)
dm/dx = 20x^4/21x^2
y = m^4
dy/dm = 4m^3
dy/dx = dm/dx * dy/dm
= 20x^4/21x^2 * 4(4x^5-1/7x^3)^3
QUESTION 6
ReplyDeletey = (5x + 7)^12
let u = 5x +7
du/dx = 5
y = U^12
dy/du = 12u^11
dy/dx = du/dx x dy/du
= 5 x 12(5x+7)^11
QUESTION 7
let h = x^2 + 3 after diff.
dh/dx of h = 2x
y = h^5
dy/dh = 5h^4
dy/dx = dh/dx X dy/dh
= 2x X 5(x^2 + 3)^4
QUESTION 8
y = (4x^2 - x)^1/2
let Z = 4x^2 - x
dz/dx = 8x - 1
y = m^1/2
dy/dz = 1/2z^-1/2
dy/dx = dz/dx X dy/dz
= (8x-1) X 1/2(4x^2 - x)^-1/2
Miss is there a problem in que.3
ReplyDeleteQuestion 6
ReplyDeletey = (5x + 7)^12
let S = 5x +7
therfore
dS/dx = 5
y = S^12
dy/dS = 12S^11
dy/dx = dS/dx * dy/dS
= 5 * 12(5x+7)^11
Question 7
y = (x^2+ 3)^5.
let S = x^2 + 3
Therefore
dS/dx = 2x
y = S^5
dy/dS = 5S^4
dy/dx = dS/dx * dy/dS
= 2x * 5(x^2 + 3)^4
Question 8
y = (4x^2 - x)^1/2
let S = 4x^2 - x
Therefore
dS/dx = 8x - 1
y = S^1/2
dy/dS = 1/2S^-1/2
dy/dx = dS/dx * dy/dS
= (8x-1) * 1/2(4x^2 - x)^-1/2
Can someone help with question 2 and 10 plez.
ReplyDeleteWhen from the info. the equation would be
ReplyDeletef=1/√C
You find for DF/DC and substitute the values. But for the other part i am not sure can anyone continue from here.
question 1
ReplyDeleteA 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?
A= πr^2
dA/dR=2πr
since r is increasing at 4
dA/dR=2π4
dA/dR=25.13
the rate at which it is flowing is : 25.13*.5= 12.57
This comment has been removed by the author.
ReplyDeletei can start Q2. but i getting stuck..here's what i got :
ReplyDeleteF = 1/k √C
subs. ... 920 = 1/k √3.5
k = 0.002
so if...F = 1/k √C
then, F = 1/k (C)^0.5
so, F = k^-1 (c)^0.5..
dont know what to do next lol...help?!
Q6.
ReplyDeletey = (5x + 7)^12
subs. m = 5x +7
therfore
dm/dx = 5
rewrite : y = m^12
so...dy/dm = 12m^11
dy/dx = dy/dm x dm/dx
hence,
dy/dx = 12(5x+7)^11 x 5 or
= 55(5x+7)^11
Q7.
ReplyDeletey = (x^2+ 3)^5.
let m = x^2 + 3
Therefore
dm/dx = 2x
rewrite : y = m^5
dy/dm = 5m^4
dy/dx = dy/dm x dm/dx
= 5(x^2 + 3)^4 x (2x) or
= 10x (x^2 + 3)^4
This comment has been removed by the author.
ReplyDeleteQ8.
ReplyDeletey = (4x^2 - x)^1/2
let p = (4x^2 - x)
Therefore
dp/dx = 8x - 1
rewrite : y = p^1/2
dy/dp = 1/2p^-0.5
dy/dx = dy/dp x dp/dx
= 1/2(4x^2 - x)^-0.5 x (8x-1)
Q9. y = (2x^3 - 1)^4
ReplyDeletetherefore,
let p = 2x^3 - 1
dp/dx = 6x^2
rewrite : y = p^4
dy/dp = 4p^3
dy/dx = dy/dp * dp/dx
= 4(2x^3-1)^3 x (6x)^2 or
= 24x^2 (2x^3-1)
Q10. y =(4x^5 - 1/(7 x^ 3))^4
ReplyDeletelet p = (4x^5 - 1)/(7x^3)
therefore:
dp/dx = 20x^4/21x^2
rewrite:
y = p^4
dy/dp = 4p^3
dy/dx = dp/dx x dy/dp
dy/dx = (20x^4/21x^2) x 4(4x^5-1/7x^3)^3
Q3.
ReplyDeletes= 490t^2
so,
ds/dt = (2 x 490)^2-1 t
ds /dt = 980 t
when t=10s
ds/dt = 980 x (10)
= 9800 cm/s or 98 m/s
Q5. Find the derivative of the function
ReplyDeletey = x^1/4 - 2/x
simplify..
y = x^1/4 - 2x^-1
hence,
dy/dx = (1/4x^ -3/4) -2 or
dy/dx = 0.25x^ -0.75 -2