Unit Test — Cumulative exam Answers

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Review the table of values for function g(x).xg(x)2.9–1.552.99–1.582.999–1.593.0011.593.011.583.11.55

A
The limits = –1.6 and = 1.6. Both and exist, so exists.
Option A
B
The limits = 1.6 and = –1.6. Both and exist, so exists.
Option B
C
The limits = –1.6 and = 1.6. Because ≠ , does not exist.
Option C
D
The limits = 1.6 and = –1.6. Because ≠ , does not exist.
Option D
3

Review the graph of the function f(x).

Question illustration
A
Limit of f (x) = 2 as x approaches 1 minus. Limit of f (x) D N E as x approaches 1 plus.
Option A
B
Limit of f (x) = negative 2 as x approaches 1 minus. Limit of f (x) D N E as x approaches 1 plus.
Option B
C
Limit of f (x) D N E as x approaches 1 minus. Limit of f (x) D N E as x approaches 1 plus.
Option C
D
Limit of f (x) D N E as x approaches 1 minus. Limit of f (x) = negative 2 as x approaches 1 plus.
Option D
4

What is ?

Question illustration
A
0
B
1
C
3
D
DNE
5

Over the closed interval [3, 8], for which function can the extreme value theorem be applied?

A
h (x) = StartFraction negative 2 Over 5 (x minus 4) squared EndFraction
Option A
B
h (x) = StartFraction (x minus 5) (x minus 1) Over x squared minus 25 EndFraction
Option B
C
h (x) = StartLayout Enlarged left-brace first row StartFraction 9 x Over 10 minus x EndFraction, x less-than 4 second row x + 2, x greater-than-or-equal-to 4 EndLayout
Option C
D
h (x) = StartLayout Enlarged left-brace first row negative x, x less-than 5 second row x squared minus 20, x greater-than-or-equal-to 5 EndLayout
Option D
8

Which function is continuous at x = 18?

A
f (x) = StartFraction (x minus 18) squared Over x EndFraction
Option A
B
f (x) = StartFraction x squared minus 17 x minus 18 Over x minus 18 EndFraction
Option B
C
f (x) = tangent (StartFraction pi Over 36 EndFraction x)
Option C
D
f (x) = StartLayout Enlarged left-brace first row x squared, x not-equals 18 second row 36, x = 18 EndLayout
Option D
9

What is ?

Question illustration
A
Negative one-sixth
Option A
B
0
C
One-sixth
Option C
D
DNE
10

Given . What is ?

Question illustration
A
–2
B
–1
C
1
D
2
11

Review the graph of a piecewise function.

Question illustration
A
jump discontinuity at x = –2; mixed discontinuity at x = 0
B
jump discontinuity at x = –2; infinite discontinuity at x = 0
C
endpoint discontinuity at x = –2; mixed discontinuity at x = 0
D
endpoint discontinuity at x = –2; infinite discontinuity at x = 0
13

What is ?

Question illustration
A
Negative one-sixth
Option A
B
0
C
One-sixth
Option C
D
DNE
14

What is ?

Question illustration
A
–16
B
–8
C
StartFraction 1 Over 16 EndFraction
Option C
D
StartFraction 1 Over 8 EndFraction
Option D
15

Review the graph of function g(x).

Question illustration
A
Limit of g (x) = 2 as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus
Option A
B
Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) = negative 2 as x approaches 4 plus
Option B
C
Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) D N E as x approaches 4 plus
Option C
D
Limit of g (x) D N E as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus
Option D
17

Given . What is ?

Question illustration
A
Negative three-halves
Option A
B
0
C
Three-halves
Option C
D
DNE
18

Which function is continuous at x = –4?

A
g (x) = StartFraction x Over (x + 4) squared EndFraction
Option A
B
g (x) = StartFraction (x + 8) (x + 4) Over x + 4 EndFraction
Option B
C
g (x) = StartLayout enlarged left-brace first row x squared, x less-than negative 4 second row negative 4 x, x greater-than-or-equal-to negative 4 EndLayout
Option C
D
g (x) = StartLayout Enlarged left-brace first row x squared minus 4, x less-than negative 4 second row 5 x, x greater-than-or-equal-to negative 4 EndLayout
Option D

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