Calculus Answers

y = e^sin x tanh^-1 (4x^2)

find dy/dx

f(x) = (archtanh √3x^2)^3

1. An observer stands 800 meters from the launch pad of a rocket, watches it       ascend vertically at 100 m/s.

a.  Find the rate of change of the distance between the rocket and the observer. (Hint: Use Pythagorean Theorem)

b. Find the distance between the observer and the rocket when the rocket is 500 meters high.

c. What is the rate of change of the distance between the rocket and the observer when the rocket is 500 meters high?

The region R is bounded by the curve "y =4-x\u00b2" and the line "y=4-2x"

   a. Find the intersection points.

b.Sketch and shade the region R.

Using the epsilon minus delta definition,show that lim X tends to 2 (3x-5)=1

Use the method cylinders to determine the volume of the solid obtained by rotating the region bounded by the given curves about the given axis of y=e^1/2 x/x+2, y=5 - 1/4 x, x=-1 abd x=6 about the line x=-2.

Find the area bounded by y = 2; y = √x + 2; and y = 2 - x

Determine the length of arc of curve 𝑦

2 = 2𝑥 (𝑓𝑜𝑟 0 ≤ 𝑥 ≤

1

2

) in the first 

quadrant.

Determine the length of curve 𝑥 =

2/3

(𝑦 − 1)raise to 3/2 when 𝑦 ∈ [1,4]

.Determine the length of curve 𝑥 =

2

3

(𝑦 − 1)

3

2 when 𝑦 ∈ [1,4]