Calculus Answers

1. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a rate of p 3 ft s, how fast is the bottom of the ladder sliding away from the building when the top of the ladder is 10 ft above the ground?

2. A sphere is growing in such a manner that its volume increases at 0:2 m³ s(cubic meter per second). How fast is its radius increasing when it is 7 m long?

Evaluate through constructing table of values

Lim In x 1-cos t/sint

t→0

Write down 𝑇3(𝑥), 𝑇4(𝑥), 𝑎𝑛𝑑 𝑇5(𝑥) for the Taylor series of 𝑓(𝑥) = ln (3 + 4𝑥) about 𝑥 = 0

Specify and sketch the domain of the following function

f(x,y)= (y^2 + x^2) / √(y^2 - x^2)

Sketch the curve y = x³-3x.

Find the equations of the tangent and the normal of y = 3x²-2x+1 at point (1,2).

Find the first derivative of y with respect to x. Use the given relation in its

implicit form.

a. x² + y² = a²

b. X² + 4y² = 4ay

Find the second derivative of y = (x2+x+1)2

Find the first derivative of y = (3x+4)2