MATH 115 EXAM 1 REVIEW

Name & Class Time:

Answer the questions in the spaces provided.You are expected to do your own work. SHOW ALL WORK.

1. Simplify the following expression:

(4a5)9(6a−4)3(10b)−1

2. Rewrite the following expression using radical notation

(x2 − 3)−1/2

MATH 115 EXAM-1

3. Rewrite the following expression using rational exponents

x√x3 + 3

4. Write the domain of the following function in interval notation

x+ 3

x− 5

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MATH 115 EXAM-1

5. Compute the following limits given the graph below of f(x)

-1 1 2 3 4

-3

-2

-1

1

2

3

4

(a) (5 points) limx→−1+ f(x)

(b) (5 points) limx→1+ f(x)

(c) (5 points) limx→−1 f(x)

(d) (5 points) limx→1 f(x)

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MATH 115 EXAM-1

6. Find each of the following limits

f(x) =

{2x+ 9, x < −23x+ 4, x > −2

(a) (5 points) limx→−2− f(x)

(b) (5 points) limx→−2+ f(x)

(c) (5 points) limx→−2 f(x)

7. Show that the function G(x) is continuous at a = 1

G(x) =

x2−xx−1 , x < 1

1 x = 1

2x− 1, x > 1

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MATH 115 EXAM-1

8. (25 points) Identify the limit property used to simplify in each step. Use the numberingpresented in class (which is the same as the textbook if you missed class).

limx→4

2 + x√x− 3

(a)=

limx→4 2 + x

limx→4

√x− 3

(b)=

limx→4 2 + limx→4 x

limx→4

√x− 3

(c)=

limx→4 2 + limx→4 x√limx→4(x− 3)

(d)=

limx→4 2 + limx→4 x√limx→4 x− limx→4 3

(e)=

limx→4 2 + 4√4− limx→4 3

(f)=

2 + 4√4− 3

=6

1= 6

(a)

(b)

(c)

(d)

(e)

(f)

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MATH 115 EXAM-1

9. Compute the following limits

(a) limx→2(x+9)3

x+1

(b) limx→1(3x5 + 4x− 2)

(c) limx→−32x2−x−21

9−x2

(d) limx→99−x√x−3

(e) limx→2x2+3x−10x2−4x+4

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MATH 115 EXAM-1

10. What are the two interpretations of the derivative?

(a)

(b)

11. Given the following function f(x) compute the following derivatives:

f(x) = x2 + 4x

(a) f ′(1)

(b) f ′(x)

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MATH 115 EXAM-1

12. Given the following function f(x) compute the following derivatives:

f(x) =1

2x+ 1

(a) f ′(1)

(b) f ′(x)

13. Given the following function f(x) compute the following derivatives:

f(x) =√2x+ 1

(a) f ′(1)

(b) f ′(x)

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MATH 115 EXAM-1

14. Based on data from Major League Baseball, the average price of a ticket to a majorleague game can be approximated by

p(x) = 0.03x3 + .56x+ 8.63

where x is the number of years after 1991 and p(x) is in dollars.

(a) Find the average rate of change of ticket prices from 1992 to 2000.

(b) Find the instantaneous rate of change of the ticket price in the year 2000.

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