Calculus Answers

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

Differentiate the function:

.F(x)= x − 4x^2 / x^3.

is

a. F′(x)= 2 / x^3 − 4 / x^2

b.F′(x)= 3x^2 − 24x

c.F′(x)= − 2 / x^3 + 4 / x^2

d.F′(x)= 1 − 8x / 3x^2

The derivative of F(x) =12xe^6x

is

a.12e^6x (1 + x)

b.12e^6x (1+ 6x^2)

c.36e^6x (1+x)

d.12e^6x (1+6x)

Find the derivative of

F(x)=14+ln  x /√ x + 5

a. 3x+10 / 2 x (x + 5)

b. x +10 / 2x (x + 5)

c. 10 / 2x ( x + 5)

d. 2x (x + 5)

Use the bissection method to approximate the root of f(x)=2x^2-1 in the interval (0,1). Let ε =0.1be the margin of error of approximation.0.1be the margin of error of approximation.