• Pasadena City College

• MATH 5A

Math 005A Score: ______/______

Exam #1 Henes Name________________________________

For full credit: Please show work, simplify all answers and use correct mathematical notation. Please circle or

box your answers. Unless otherwise specified, each problem is worth 5 points.

1. Evaluate the difference quotient !(#$%)'!(#)

%

for the given function.

(()) = 1

) + 1

2. Sketch the graph of a function g with the following properties.

O

3. a) Sketch the graph of the function, b) give its domain, and c) state where the function is

continuous. a)

(()) = :2) + 3 if ) ≤ -1

)1 + 2 if ) > -1

b)

c)

4. Find the following limits (if they exist) for the function given in #3.

a) lim

#→'?5

(()) b) lim

#→'?7

(()) c) lim

#→'?

(())

5. Find each limit, if it exists.

6. Find each limit, if it exists. Be sure to justify your answer. (No points for guessing.)

lim

#→1

√#A$?1'B

#'1

lim

#→F

)B sin ?

#

7. Find each infinite limit. Be sure to justify your answer. (No points for guessing.)

lim

#→17

#$4

1'#

lim

#→(I/1)5

) sec )

8. Find the limit L for lim

#→1

(4) - 1) = N. Then find O > 0 such that (()) is within P = 0.01

of L.

9. Explain why the equation )4 - 3) = cos ) has at least one solution. (Hint: If you use a

theorem, name the theorem and verify that any hypotheses are satisfied.)

10. Determine c so that the function is continuous everywhere.

(()) = S)1 - T if ) < 5

4) + 2T if ) ≥ 5

11. Express the absolute value function as a piecewise-defined function.

(()) = |5 - 3)|