Need A Few MATH PROBLEMS (calculus) Completed Tonight for $15 Paypal

21. A particle moves along the x-axis so that at any time t≥0, its velocity is given by v(t)=3+4.1cos(0.9t). What is the acceleration of the particle at the time t=4?

22. The position equation for the movement of a particle is given by s=(t^2-1)^3 when s is measured in feet and f is measured in seconds. Find the acceleration at two seconds.

23. The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20Ï€ meters?

Ï€=pi

24. Find the value of C that satisfies the Mean Value Theorem for f(x)=xsinx on [1,4]

25. Let f be a function with derivative given by f'(x)=sin(x^2+1). How many relative extrema does f have on the interval 2<x<4?

26. The function f has first derivative given by f'(x)= (x^1/2)/(1+x+x^3). What is the x-coordinate of the inflection point of the graph of f?

(x^1/2)=square root of x

27. solved

28. solved

29. http://i48.tinypic.com/34t2ts0.jpg


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21. Get the derivative of v(t) then plug in t=4 (acceleration is the derivative of speed)

v'(t) = -4.1 sin(0.9t) * 0.9 ----> plugin t =4 here

22. Same with #21. Get derivative of s. then plug in t=2

let x = t^2-1
d(x) = 2t

s = x^3

s' = 3x^2 * d(x)

s' = 3(t^2-1)^2 * 2t ---> substitute t = 2 here



23. d(r) = (r + 0.2) m/s ----> rate of increase of r


Get value of r when C = 20(pi)

C = 2 (pi) r ----> formula for circumference

r = C / 2 (pi)

r = 20 (pi) / 2 (pi)

r = 10



Get d(A) --> derivative of area of circle (rate of increase of the area)


A = (pi)r^2

d(A) = 2 (pi) r * d(r)

d(A) = 2 (pi) r * (r + 0.2) m/s

substitute r = 10 to the above equation to get d(A)