Prof. Israel N. Nwaguru
MATH 1325
EXAM 1
REVIEW
WORK OUT EACH PROBLEM NEATLY AND ORDERLY BY SHOWING ALL THE STEPS AS
INDICATED IN CLASS ON SEPARATE SHEET, THEN CHOSE THE BEST ANSWER.
TO EARN ANY CREDIT, YOU MUST SHOW WORK.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use a calculator to estimate the limit.
x 2 + 5x - 14
1) lim
x -7 x 2 + 13x + 42
Answer:
9
1
Objective: (11.1) Use Calculator: Estimate Limit
x-9
2) lim
x 1 x - 81
Answer:
1
10
Objective: (11.1) Use Calculator: Estimate Limit
Use the limit properties to find the following limit.
3) If
x
lim
-1
Answer:
f(x) = 4 and
x
lim
-1
g(x) = 14, find
x
f(x) + g(x)
.
6g(x)
-1
lim
3
14
Objective: (11.1) Use Limit Properties to Find Limit
Use the properties of limits to evaluate the limit if it exists.
lim
x- 7
4)
x 49 x - 49
Answer: Does not exist
Objective: (11.1) Use Algebra to Find Limit
5)
lim x 2 - 2x - 15
x -3
x+3
Answer: -8
Objective: (11.1) Use Algebra to Find Limit
Find the average rate of change for the function over the given interval.
6) y = x3 + x2 - 8x - 7 between x = 0 and x = 2
Answer: -2
Objective: (11.2) Find Average Rate of Change for Function
1
7) y = -3x2 - x between x = 5 and x = 6
Answer: -34
Objective: (11.2) Find Average Rate of Change for Function
Find f'(x) for the function, then find f'(x) for the given x.
8) g(x) = 4x - x 3 , g'(2)
Answer: g'(x) = 4 - 3x 2 ; g'(2) = -8
Objective: (11.3) Find f'(x) and f'(a) for Given a
Find the derivative.
9) y = 13x -2 + 15x 3 - 2x
Answer: -26x -3 + 45x 2 - 2
Objective: (11.4) Find Derivative of Function
Find the derivative of the function.
10) f(x) = (5x - 3)(2x 3 - x2 + 1)
Answer: f'(x) = 40x 3 - 33x 2 + 6x + 5
Objective: (11.5) Use Product Rule to Find Derivative
11) f(x) = (2x - 3)( x + 2)
Answer: f'(x) = 3x 1/2 - 1.5x -1/2 + 4
Objective: (11.5) Use Product Rule to Find Derivative
Use the quotient rule to find the derivative.
x 2 - 3x + 2
12) y =
x7 - 2
Answer: y' =
-5x8 + 18x7 - 14x6 - 4x + 6
(x7 - 2)2
Objective: (11.5) Use Quotient Rule to Find Derivative
13) g(x) =
x2 + 5
x 2 + 6x
Answer: g'(x) =
6x2 - 10x - 30
x 2 (x + 6)2
Objective: (11.5) Use Quotient Rule to Find Derivative
Find the derivative.
(6x - 5)(2x - 4)
14)
6x - 3
Answer:
72x 2 - 72x - 18
(6x - 3) 2
Objective: (11.5) Use Product and Quotient Rules to Find Derivative
2
Find the derivative of the function.
15) y = (4x + 3)5
Answer: y' = 20(4x + 3)4
Objective: (11.6) Find Derivative of Function
16) y = 4x + 2
Answer: y' =
2
4x + 2
Objective: (11.6) Find Derivative of Function
17) y = (3x2 + 5x + 1)3/2
Answer: y' =
3
(6x + 5)(3x2 + 5x + 1)1/2
2
Objective: (11.6) Find Derivative of Function
18) g(x) =
x2 + 5
x 2 + 6x
Answer: g'(x) =
6x2 - 10x - 30
x 2 (x + 6)2
Objective: (11.6) Use Product or Quotient Rule to Find Derivative
Find the derivative.
19) y = -10e-6x
Answer: 60e-6x
Objective: (11.7) Find Derivative of Exponential Function
20) y = e9x 2 + x
Answer: 18xe9x 2 + 1
Objective: (11.7) Find Derivative of Exponential Function
21) y =
7ex
2ex + 1
Answer:
7ex
(2ex + 1)2
Objective: (11.7) Find Derivative of Exponential Function
22) y = 5x2 e3x
Answer: 5xe3x(3x + 2)
Objective: (11.7) Find Derivative of Exponential Function
3
Find the derivative of the function.
23) y = ln 9x 2
Answer:
2
x
Objective: (11.7) Find Derivative of Logarithmic Function
24) y = ln (2x 3 - x2 )
Answer:
6x - 2
2x 2 - x
Objective: (11.7) Find Derivative of Logarithmic Function
25) y = ln 2x
Answer:
1
x
Objective: (11.7) Find Derivative of Logarithmic Function
Find all points where the function is discontinuous.
26)
Answer: x = -2, x = 2
Objective: (11.8) Find All Points of Discontinuity Given Graph
Of the given values of x, identify those at which the function is continuous.
5
; x = -6, 0
27) f(x) =
x+6
Answer: 0
Objective: (11.8) Determine Whether Function Is Continuous at Given x
28) f(x) =
x 2 - 49
; x = -7, 0, 7
x-7
Answer: -7, 0
Objective: (11.8) Determine Whether Function Is Continuous at Given x
4
Decide whether or not the function is continuous in the indicated x-interval.
29) -3 to 0
Answer: Continuous
Objective: (11.8) Choose Interval on Which Function Is Continuous
30) -4 to 0
Answer: Not continuous
Objective: (11.8) Choose Interval on Which Function Is Continuous
5