## Practice Problems

Work through the odd-numbered problems 1-59. Once you have completed the problem set, check your answer

### Problems

1. Fig. 9 shows and for . Let .

(a) At what value of does have a root?

(b) Determine the limits of as , and ,

(c) Where does have a vertical asymptote?

**Fig. 9**

3. Fig. 11 shows and for . Let , and determine the limits of as , and .

**Fig. 11**

For problems 5-23, calculate the limit of each expression as " ".

25. Salt water with a concentration of pounds of salt per gallon flows into a large tank that initially contains gallons of pure water.

(a) If the flow rate of salt water into the tank is gallons per minute, what is the volume of water and the amount of salt in the tank t minutes after the flow begins?

(b) Show that the salt concentration at time is .

(c) What happens to the concentration after a "long" time?

(d) Redo parts for a large tank which initially contains gallons of pure water.

For problems 27-41, calculate the limits.

In problems 43-49, write the **equation** of each asymptote for each function and state whether it is a vertical or horizontal asymptote.

In problems 51-59, write the **equation** of each asymptote for each function.