Review questions for exam 1.

(i) Find the limit. (Possible answers include or ‘DNE’)

(a)

(b)

(ii) Let be a function such that .

(a) Find the limit or say ‘DNE’:

(a)

(b)

(c)

(d)

(ii) Find all vertical asymptotes of f:

(iii) Find all horizontal asymptotes of f:

(iv) List the (largest) intervals of continuity of f:

Let . Since is a

monotonecontinuous function for all in the interval , and 01 is between -1f(-1)=-3 and 0f(0)=2 , then the IVT guarantees the existence of at least one number uf(u) in such that f(u) = 0f(0) = u .(i) Evaluate the following expressions:

(a)

(b)

(ii) Determine if the following statements are true or false:

(a) Given a one-to-one function and its inverse , , where x is in the domain of .

(b) .

(c) Given .

(iii) Find the inverse of .

(iv) Use a right triangle to simplify .

- (a)
- Find expressions for on the following intervals:
- (i)
- For ,
- (ii)
- For ,

- (b)
- Find the values or write DNE.

The (entire) graph of a function is given in the figure below.

(i) Find the domain and range of . Write your answer in interval notation.

Domain of :

Range of :

(ii) List the largest intervals of continuity for : and and

(a) exists, but the function is NOT continuous at .

The (entire) graph of a function is given in the figure below.

(a) Find the domain and range of

Domain:

Range:

(b) Which of the following represents the graph of

(c) Find the following limits or say that a limit does not exist (DNE).

(i)

(ii)

(iii)

(iv)

(d) List all the intervals of continuity:

(e) Find the following values or expressions, or say ‘DNE’.

(i)

(ii) For ,

(f) Find the domain of :

(g) Find the expression for , for .

Choose the correct (complete) graph of .

(a) A function is defined on the interval . , and the following inequality holds:

Select the correct limit, and justification:

(b) A function is defined on the interval , and the following inequality holds:

Select the correct limit and justification:

The function is defined by .

(a) Is the function defined on :

(b) Find the domain of :

(c) Is the function odd, even, or neither:

(d) Find all horizontal asymptotes.

(e) Find all vertical asymptotes.

Let

(i) Determine if the following limits exist. If they do, compute them analytically using the limit laws and techniques discussed in class. If they don’t, say ‘DNE’. [You may not use a table of values, a graph, or L’Hospitals rule to justify your answer.]

(a)

(b)

(c)

(d)

(ii) Find all vertical asymptotes of or say ‘none’:

(iii) Find all horizontal asymptotes of or say ‘none’:

(iv) Find the (largest) intervals of continuity of :