Calculus Answers

Suppose that in t hours, a truck travels s(t) miles, where s(t)= 10t² . Find the average rate of change of distance with respect to time from t1 = 2 and t2 = 5.

The volume of a cube is increasing at a rate of 1200 cm3/min at the

moment the lengths of the sides are 20 cm. How fast are the lengths of

the sides increasing at that moment?

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1. Let f be the function defined by

f (x) = x2

-------------

(2x + 1)2

:

(a) Determine the vertical and horizontal asymptotes (show all limits). (4)

(b) Use the sign pattern for f ' (x) to determine

(i) the interval(s) over which f rises and where it falls; (4)

(ii) the local extrema. (2)

(c) Use the sign pattern for f " (x) to determine

(i) where the graph of f is concave up and where it is concave down. (4)

(ii) the inflection points (if any) (2)

Find the area of the surface generated by revolving the curve y=√25-x², from x = - 2 to x = 3 , about the x-axis.

Find the length of the arc with the curve

y = 2x ^ (3/2) between x = 1/3 and x = 7

An unstretched spring is 10 ft long. A pull of 40 lb stretches the

spring by ½ ft. Find the work done in stretching the spring from

10 ft to 14 ft.

a rectangle is inscribed under the curve y=2^-x with its base along the positive x-axis. Find the dimensions of the rectangle with the largest area

Find the derivative of the function

P(x)=ln ⁡[ (4x + 1)^3 / (2x − 5)^4 ]

is

a. −4(2x−17) / (4x+1)(2x−5)

b.−4(2x−17) / (4x+1)

c. 4(−2x−17) / (4x+1)(2x−5)

d. (−2x−17) / (4x+1)(2x−5)

Find the second derivative of the following function:

F(x)=3x^3 − 1 / x + e^2x.

is

a.18x − ln x + 4e^2x

b.18x − 2 / x^3 + 2e^2x

c.18x + 2 / x^3 + 4e^2x

d.18x − 2 / x^3+ 4e^2x

Find the derivative of the function:

x^5 e^3x + x + 1 / x

a. x^5 e^3x + 5x^4 e^3x + 1 / x^2

b.3x^5 e^3x + 5x^4 e^3x − 1 / x^2

c. x^5 e^3x + 5x^4 e^3x − 1 / x^2

d. 3x^5 e^3x + 5x^4 e^3x − 2 / x