Functions Derivative Integrals Evaluations & Tangent Line Calculus Questions 1) Find all the solutions of the following equation. 2) Determine the followi

Functions Derivative Integrals Evaluations & Tangent Line Calculus Questions 1) Find all the solutions of the following equation.

2) Determine the following limits.

a)

b)

c) Based on your results, does the function have a horizontal asymptote? If yes, what is it?

3) Find the derivative of each function.

a)

b) y

c)

4) Find the equation of the tangent line to the given curve at the given point .

5) Find the absolute maximum and absolute minimum values (if they exist).

6) Given f ( x ) = x 2 + 3 x − 1

a) Find Domain.

b) Find Vertical and Horizontal Aysmptotes.

c) Find intervals of increasing and decreasing.

d) Find local maximum and minimum points.

e) Find intervals of concave up and concave down.

f) Find inflection points.

g) Sketch the graph.

7) Explain why the Mean Value Theorem does not apply to the function.

8) Evaluate the following limits using l’Hopital’s Rule.

a)

b)

9) Evaluate the following integrals.

a)

b)

c)

d)

10) A spherical balloon is inflated and its volume increases at a rate of 15 cubic inches per minute. What is the rate of change of its radius when the radius is 10 inches?

11) Evaluate the following derivative.

13) Find the derivative of

14) Use the precise definition of a limit to prove [Use ε a n d δproof and be sure to show all your steps in detail.]

15) Find positive numbers x and y satisfying the equation such that the sum is as small as possible