Question

Please solve and show work when necessary:

1. What is the definition of a limit?

2. What are the 8 properties of a limit?

3. What does it mean to be indeterminate?

4. What is the definition of a Vertical Asymptote and how do you find the vertical asymptote ( Hint their a 2 cases)

5. What is a Horizontal Asymptote and what are the 3 cases in determining the horizontal asymptote?

6. What is the definition of continuity?

7. What is the definition of the derivative? ( Hint: its the limit of...?)

8. What are the 3 interpretations of the derivative?

9. What are the 4 steps to finding the derivative of the function?

10. What are the 4 theorems for taking the derivative explained in this section?

11. Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. (Hint: Find the derivative of the function)
C(x) = 0.0002x3 - 0.048x2 + 200x + 50,000
R(x) = 400x

Answer 1

1. definition of limit: a function f(x) defined on an interval that contains x=a ,then we say that, limit is for 0< |x−a|< δ

2. Properties of limit:a) Addition/subtraction:

b) Constant multiple:

c) Product rule:

d) Quotient rule:

e) Power rule:

f)

g)

h)

3. Indeterminate: means a mathematical expression which is not precisely defined .

4. Vertical Asymptote : It is a vertical line to which graph of a function approaches. These vertical lines correspond to the zeroes of the denominator in rational function.
To find vertical asymptote, equate the denominator of function to Zero. The x values you will get,those will be vertical asymptotes.