Calculus Answers

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.

state the statement is true or false the function f[x,y]={x^2y/x^4+y^2[x,y]=0 is not continuous at [0,0] and 0,[x,y]=0

Use the bissection method to approximate the root of f(x)=2x²-1 in the interval . Let ε=0.1 be the margin of error of approximation.

Calculate the surface area Integral of object obtained by rotating the function x=2y+5 for x=-1 and -2 about y axis

If c>0, then the following equality holds,

the integral from a to b dx/x equals to the integral from ac to bc dx/x.

Show your work and an explanation for each step.

F(x) = "\\smallint" "(x+9)dx \/ (x-2)(x+2)"² and F(3.1) = 5.5. Compute F( -0.5)

A projectile is launched vertically upward from the ground level with an initial velocity of 16 ft/s.

a. How long will it take for the projectile to hit the ground?

b. How long will the projectile be moving upward?