Deck 2: Limits and Continuity

Question 1

Let $f ( x ) = \left\{ \begin{array} { c c } 2 x - 5 & x < 4 \\0 & x = 4 \\\frac { x } { 2 } & x > 4\end{array} \right.$ . Which of the following is true for $\lim _ { x \rightarrow 4 } f ( x )$ ?

A)3
B)2
C)0
D)1
E)Does not exist

Answer 1

Does not exist

Question 2

Let $f ( x ) = \left\{ \begin{array} { c c } - 2 x + 1 & - 3 \leq x < - 1 \\4 & x = - 1 \\x - 2 & - 1 < x < 7\end{array} \right.$ . Which of the following is true for $\lim _ { x \rightarrow - 1 } f ( x )$ ?

A)-3
B)1
C)3
D)4
E)Does not exist

Answer 2

Does not exist

Question 3

Let $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } - 1 & - 3 \leq x < 0 \\3 x & 0 < x < 3 \\2 x - 5 & 3 < x < 10\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow 0 } f ( x )$ ?

A)-3
B)1
C)3
D)4
E)Does not exist

Answer 3

Does not exist

Question 4

Let $f ( x ) = \left\{ \begin{array} { c c } \frac { 9 } { x } & - 5 < x < - 3 \\2 & x = - 3 \\x & - 3 < x < 1\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow - 3 } f ( x )$ ?

A)-3
B)2
C)3
D)5
E)Does not exist

Question 5

Let $f ( x ) = \left\{ \begin{array} { c c } 3 x - 1 & x < 1 \\0 & x = 1 \\\frac { 2 } { x } & x > 1\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow 1 } f ( x )$ ?

A)0
B)1
C)2
D)3
E)Does not exist

Question 6

Let $f ( x ) = \left\{ \begin{array} { c l } 2 x ^ { 2 } & x < - 2 \\4 & x = - 2 \\x + 10 & x > - 2\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow - 2 } f ( x )$ ?

A)4
B)6
C)8
D)10
E)Does not exist

Question 7

Let $f ( x ) = \left\{ \begin{array} { c c } 3 x & - 1 < x < 0 \\x + 4 & 0 \leq x < 4 \\2 x & 4 < x \leq 7\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow 4 } f ( x )$ ?

A)-3
B)0
C)4
D)8
E)Does not exist

Question 8

Let $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x \leq 2 \\1 + x & x > 2\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow 2 } f ( x )$ ?

A)-1
B)1
C)2
D)-2
E)Does not exist

Question 9

Let $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & - 6 < x < - 4 \\2 & x = - 4 \\6 x + 8 & - 4 < x \leq 7\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow - 4 } f ( x )$ ?

A)-16
B)0
C)2
D)16
E)Does not exist

Question 10

Let $f ( x ) = \left\{ \begin{array} { c c } - x ^ { 2 } + 2 & - 3 < x < 0 \\3 & x = 0 \\2 x + 4 & 0 < x \leq 3\end{array} \right.$ Which of the following is true for $\lim _ { x \rightarrow 0 } f ( x )$ ?

A)2
B)3
C)4
D)0
E)Does not exist

Question 11

Let $f ( x ) = \lfloor x \rfloor + 3$ Which of the following is true for $\lim _ { x \rightarrow 0 ^ { - } } f ( x )$ ?

A)2
B)3
C)4
D)5
E)Does not exist

Question 12

Let $f ( x ) = \lfloor x \rfloor + 3$ Which of the following is true for $\lim _ { x \rightarrow 0 ^ { + } } f ( x )$ ?

A)2
B)3
C)4
D)5
E)Does not exist

Question 13

Let $f ( x ) = \sqrt { x + 1 }$ Which of the following is true for $\lim _ { x \rightarrow 1 ^ { + } } f ( x )$ ?

A)-1
B)0
C)1
D) $\sqrt { 2 }$
E)Does not exist

Question 14

Let $f ( x ) = \sqrt { x + 1 }$ Which of the following is true for $\lim _ { x \rightarrow - 1 ^ { - } } f ( x )$ ?

A)-1
B)0
C)1
D) $\sqrt { 2 }$
E)Does not exist

Question 15

Let $f ( x ) = 2 \lfloor x \rfloor - 3$ Which of the following is true for $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$ ?

A)-3
B)-2
C)-1
D)0
E)Does not exist

Question 16

Let $f ( x ) = 2 \lfloor x \rfloor - 3$ Which of the following is true for $\lim _ { x \rightarrow 1 ^ { + } } f ( x )$ ?

A)-3
B)-2
C)-1
D)0
E)Does not exist

Question 17

Let $f ( x ) = \lfloor x \rfloor + 1$ Which of the following is true for $\lim _ { x \rightarrow 1 ^ { + } } f ( x )$ ?

A)0
B)1
C)2
D)3
E)Does not exist

Question 18

Let $f ( x ) = \lfloor x \rfloor + 1$ Which of the following is true for $\lim _ { x \rightarrow 1 ^ { - } } f ( x )$ ?

A)0
B)1
C)2
D)3
E)Does not exist

Question 19

Let $f ( x ) = \frac { | x | } { x }$ Which of the following is true for $\lim _ { x \rightarrow 0 ^ { - } } f ( x )$ ?

A)-1
B)0
C)1
D)2
E)Does not exist

Question 20

Let $f ( x ) = \frac { | x | } { x }$ Which of the following is true for $\lim _ { x \rightarrow 0 ^ { + } } f ( x )$ ?

A)-1
B)0
C)1
D)2
E)Does not exist

Question 21

Let $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 3 }$ Which of the following is true for $\lim _ { x \rightarrow 3 } f ( x )$ ?

A)0
B)3
C)6
D)9
E)Does not exist

Question 22

Let $f ( x ) = \frac { x ^ { 2 } - 3 x - 4 } { 2 x ^ { 2 } - x - 3 }$ Which of the following is true for $\lim _ { x \rightarrow - 1 } f ( x )$ ?

A)-1
B)0
C)1
D)2
E)Does not exist

Question 23

Let $f ( x ) = \frac { x ^ { 2 } + 2 x } { 2 x ^ { 2 } + x - 6 }$ Which of the following is true for $\lim _ { x \rightarrow - 2 } f ( x )$ ?

A) $- \frac { 2 } { 7 }$
B)0
C) $\frac { 2 } { 7 }$
D)1
E)Does not exist

Question 24

Let $f ( x ) = \frac { x ^ { 3 } - 27 } { x ^ { 2 } - 9 }$ Which of the following is true for $\lim _ { x \rightarrow 3 } f ( x )$ ?

A)9
B) $\frac { 9 } { 2 }$
C)-9
D) $- \frac { 9 } { 2 }$
E)Does not exist

Question 25

Let $f ( x ) = \frac { x ^ { 3 } + 8 } { x ^ { 2 } - 4 }$ Which of the following is true for $\lim _ { x \rightarrow - 2 } f ( x )$ ?

A)3
B) $\frac { 3 } { 2 }$
C)-3
D) $- \frac { 3 } { 2 }$
E)Does not exist

Question 26

Let $f ( x ) = \frac { \sqrt { x } - 1 } { x - 1 }$ Which of the following is true for $\lim _ { x \rightarrow 1 } f ( x )$ ?

A) $- \frac { 1 } { 2 }$
B)0
C)2
D) $\frac { 1 } { 2 }$
E)Does not exist

Question 27

Let $f ( x ) = \frac { \sqrt { x + 3 } - \sqrt { 3 } } { x }$ Which of the following is true for $\lim _ { x \rightarrow 0 } f ( x )$ ?

A) $- \frac { \sqrt { 3 } } { 6 }$
B)0
C) $\frac { \sqrt { 3 } } { 6 }$
D)1
E)Does not exist

Question 28

Let $f ( x ) = \frac { \sqrt { 3 x + 1 } - 2 } { 1 - x }$ Which of the following is true for $\lim _ { x \rightarrow 1 } f ( x )$ ?

A) $- \frac { 3 } { 4 }$
B) $- \frac { 1 } { 4 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 3 } { 4 }$
E)Does not exist

Question 29

Let $f ( x ) = \frac { \sqrt { 3 x + 6 } - 3 } { 1 - x ^ { 2 } }$ Which of the following is true for $\lim _ { x \rightarrow 1 } f ( x )$ ?

A) $- \frac { 3 } { 4 }$
B)-4
C) $\frac { 1 } { 4 }$
D)4
E)Does not exist

Question 30

Let $f ( x ) = \frac { 5 - \sqrt { 2 x + 5 } } { x - 10 }$ Which of the following is true for $\lim _ { x \rightarrow 10 } f ( x )$ ?

A) $- \frac { 1 } { 10 }$
B) $- \frac { 1 } { 5 }$
C) $\frac { 1 } { 10 }$
D) $\frac { 1 } { 5 }$
E)Does not exist

Question 31

Let $f ( x ) = \frac { \frac { 1 } { x } - 1 } { 1 - x }$ Which of the following is true for $\lim _ { x \rightarrow 1 } f ( x )$ ?

A)-1
B)0
C) $\frac { 1 } { 2 }$
D)1
E)Does not exist

Question 32

Let $f ( x ) = \frac { \frac { 3 } { x + 4 } - 1 } { 1 + x }$ Which of the following is true for $\lim _ { x \rightarrow - 1 } f ( x )$ ?

A) $- \frac { 1 } { 5 }$
B) $- \frac { 1 } { 3 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 1 } { 3 }$
E)Does not exist

Question 33

Let $f ( x ) = \frac { \frac { 8 } { 3 x - 4 } - 4 } { x - 2 }$ Which of the following is true for $\lim _ { x \rightarrow 2 } f ( x )$ ?

A)-6
B)-4
C)4
D)6
E)Does not exist

Question 34

Let $f ( x ) = \frac { \frac { 3 } { 2 x } + \frac { 1 } { 2 } } { 3 + x }$ Which of the following is true for $\lim _ { x \rightarrow - 3 } f ( x )$ ?

A) $- \frac { 1 } { 4 }$
B) $- \frac { 1 } { 6 }$
C) $\frac{1}{4}$

D) $\frac { 1 } { 6 }$
E)Does not exist

Question 35

Let $f ( x ) = \frac { \frac { 6 } { 5 x } - \frac { 3 } { 5 } } { 2 - x }$ Which of the following is true for $\lim _ { x \rightarrow 2 } f ( x )$ ?

A) $- \frac { 1 } { 10 }$
B) $- \frac { 3 } { 10 }$
C) $\frac { 1 } { 10 }$
D) $\frac { 3 } { 10 }$
E)Does not exist

Question 36

Let $f ( x ) = x ^ { 2 }$ Which of the following is equal to $\lim _ { h \rightarrow 0 } \frac { f ( 3 + h ) - f ( 3 ) } { h }$ ?

A)-6
B)-2
C)2
D)6
E)Does not exist

Question 37

Let $f ( x ) = \frac { 3 } { x ^ { 2 } }$ Which of the following is equal to $\lim _ { h \rightarrow 0 } \frac { f ( - 2 + h ) - f ( - 2 ) } { h }$ ?

A) $- \frac { 3 } { 4 }$
B) $- \frac { 4 } { 3 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 4 } { 3 }$
E)Does not exist

Question 38

Let $f ( x ) = 3 x ^ { 2 } - 5$ Which of the following is equal to $\lim _ { h \rightarrow 0 } \frac { f ( 1 + h ) - f ( 1 ) } { h }$ ?

A)-6
B)-1
C)1
D)6
E)Does not exist

Question 39

Let $f ( x ) = \sqrt { x }$ Which of the following is equal to $\lim _ { x \rightarrow 4 } \frac { f ( x ) - f ( 4 ) } { x - 4 }$ ?

A) $- \frac { 1 } { 4 }$
B) $\frac { 1 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$
E)Does not exist

Question 40

Let $f ( x ) = \frac { 3 } { x + 1 }$ Which of the following is equal to $\lim _ { x \rightarrow 1 } \frac { f ( x ) - f ( 1 ) } { x - 1 }$ ?

A) $- \frac { 3 } { 4 }$
B) $- \frac { 3 } { 2 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 3 } { 2 }$
E)Does not exist

Question 41

Let $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 1 }$ Which of the following is true?

A)ƒ is defined at 1.
B)ƒ is defined at -1.
C)ƒ has a removable discontinuity at -1.
D)ƒ has a removable discontinuity at 1.
E)ƒ is continuous at -1.

Question 42

Let $f ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }$ . Which of the following is true?

A)ƒ is defined at -2.
B)ƒ is defined at 2.
C)ƒ has a removable discontinuity at -2.
D)ƒ has a removable discontinuity at 2.
E)ƒ is continuous at -2.

Question 43

$\text { Let } f ( x ) = \frac { x ^ { 3 } + 1 } { x ^ { 2 } - 2 x - 3 }$ Which of the following is true?

A)ƒ is defined at -1.
B)ƒ is defined at 3.
C)ƒ has a removable discontinuity at -1.
D)ƒ has a removable discontinuity at 3.
E)ƒ is continuous at -1.

Question 44

Let $f ( x ) = \frac { \sqrt { 4 - x } - 2 } { x ^ { 2 } + x }$ Which of the following is true?

A) . $f$ is defined at -1
B) $f$ is defined at 0.
C) $f$ has a removable discontinuity at -1.
D) $f$ has a removable discontinuity at 0.
E) $f$ is continuous at 0.

Question 45

Let $f ( x ) = \lfloor x \rfloor$ Which of the following is true?

A)ƒ is undefined at 0.
B)ƒ is undefined at $- \frac { 1 } { 2 }$
C)ƒ has a removable discontinuity at 0.
D)ƒ has a removable discontinuity at $\frac { 1 } { 2 }$
E)ƒ has a jump discontinuity at 0.

Question 46

Let $f ( x ) = \frac { | x | } { x }$ Which of the following is true?

A)ƒ is defined at 0.
B)ƒ is discontinuous at -1.
C)ƒ has a removable discontinuity at 0.
D)ƒ has a removable discontinuity at -1.
E)ƒ has a jump discontinuity at 0.

Question 47

Let $f ( x ) = \frac { | x | } { 5 x }$ Which of the following is true?

A)ƒ is defined at 0.
B)ƒ is discontinuous at -1.
C)ƒ has a removable discontinuity at 0.
D)ƒ has a removable discontinuity at -1.
E)ƒ has a jump discontinuity at 0.

Question 48

Let $f ( x ) = \left\{ \begin{array} { l l } 1 - x & x < 0 \\1 + x & x > 0\end{array} \right.$ Then ƒ is continuous at 0 if ƒ(0) is defined as

A)-2
B)-1
C)0
D)1
E)2

Question 49

Let $f ( x ) = \left\{ \begin{array} { c c } 2 x - 5 & x < 4 \\4 & x = 4 \\x - 1 & x > 4\end{array} \right.$ Then is continuous at 1 if ƒ(4) is redefined as

A)-1
B)0
C)1
D)2
E)3

Question 50

Let $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & - 3 \leq x < 0 \\3 x & 0 < x < 3 \\2 x - 5 & 3 < x < 10\end{array} \right.$ Then ƒ is continuous at 0 if ƒ(0) is defined as

A)-2
B)-1
C)0
D)1
E)2

Question 51

Let $f ( x ) = \left\{ \begin{array} { c l } 2 x ^ { 2 } & x < - 2 \\4 & x = - 2 \\x + 10 & x > - 2\end{array} \right.$ Then ƒ is continuous at -2 if ƒ(-2) is redefined as

A)4
B)5
C)6
D)7
E)8

Question 52

Let $f ( x ) = \left\{ \begin{array} { c c } 3 x & - 1 < x < 0 \\x + 4 & 0 \leq x < 4 \\2 x & 4 < x \leq 6\end{array} \right.$ Then ƒ is continuous at 4 if ƒ(4) is defined as

A)4
B)5
C)6
D)7
E)8

Question 53

Let $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } + 5 x & x < - 1 \\0 & x = - 1 \\x - 3 & x > - 1\end{array} \right.$ Then ƒ is continuous at -1 if ƒ(-1) is redefined as

A)-5
B)-4
C)-3
D)-2
E)-1

Question 54

Let $f ( x ) = \left\{ \begin{array} { c c } \frac { x } { 3 } & x < - 3 \\x + 2 & x > - 3\end{array} \right.$ Then ƒ is continuous at -3 if ƒ(-3) is defined as

A)-4
B)-3
C)-2
D)-1
E)0

Question 55

The largest set on which $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 1 }$ is continuous is

A) $( - \infty , \infty )$
B) $( - \infty , 1 ) \cup ( 1 , \infty )$
C) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
D) $( - \infty , - 1 ) \cup ( 1 , \infty )$
E) $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$

Question 56

The largest set on which $f ( x ) = \frac { x } { ( x + 1 ) ^ { 2 } }$ is continuous is

A) $( - \infty , \infty )$
B) $( - \infty , 1 ) \cup ( 1 , \infty )$
C) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
D) $( - \infty , - 1 ) \cup ( 1 , \infty )$
E) $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$

Question 57

The largest set on which $f ( x ) = \frac { x + 4 } { | x + 4 | }$ is continuous is

A) $( - \infty , \infty )$
B) $( - \infty , - 4 ) \cup ( - 4 , \infty )$
C) $( - \infty , 4 ) \cup ( 4 , \infty )$
D) $( - \infty , - 4 ) \cup ( 4 , \infty )$
E) $( - \infty , - 4 ) \cup ( - 4,4 ) \cup ( 4 , \infty )$

Question 58

The largest set on which $f ( x ) = \frac { 5 x + 3 } { 5 x ^ { 2 } + 3 }$ is continuous is

A) $( - \infty , \infty )$
B) $\left( - \infty , - \frac { 3 } { 5 } \right) \cup \left( - \frac { 3 } { 5 } , \infty \right)$
C) $\left( - \infty , \frac { 3 } { 5 } \right) \cup \left( \frac { 3 } { 5 } , \infty \right)$
D) $\left( - \infty , - \frac { 3 } { 5 } \right) \cup \left( \frac { 3 } { 5 } , \infty \right)$
E) $\left( - \infty , - \frac { 3 } { 5 } \right) \cup \left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right) \cup \left( \frac { 3 } { 5 } , \infty \right)$

Question 59

The largest set on which $f ( x ) = \sqrt { x ^ { 2 } + 1 }$ is continuous is

A) $( - \infty , \infty )$
B) $( - \infty , 1 ) \cup ( 1 , \infty )$
C) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
D) $( - \infty , - 1 ) \cup ( 1 , \infty )$
E) $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$

Question 60

The largest set on which $f ( x ) = \sqrt { x + 4 }$ is continuous is

A) $( - \infty , \infty )$
B) $( - 4 , \infty )$
C) $( 4 , \infty )$
D) $[ - 4 , \infty )$
E) $[ 4 , \infty )$

Question 61

Use the Intermediate Value Theorem to approximate the point of intersection of the function g(x) = x⁴- 2x and y = 1 in the interval (-1, 0).
​

A)-1.0
B)-0.602
C)-0.475
D)0.515
E)1.392

Question 62

Use the Intermediate Value Theorem to approximate the point of intersection of the function g(x) = $\frac { x ^ { 3 } + 1 } { x - 2 }$ and y = -1.9 in the interval (-3, 3).

A)-2.025
B)0.979
C)1.005
D)1.502
E)2.025

Question 63

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { x }$ ?

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 5 }$
C)-5
D)5
E)Does not exist

Question 64

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \cos x } { e ^ { x } }$ ?

A)-1
B)0
C)1
D)2
E)Does not exist

Question 65

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \tan ( 2 x ) } { x }$ ?

A)1
B)2
C)-1
D)-2
E)Does not exist

Question 66

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { 1 - \cos ^ { 2 } x } { 5 x }$ ?

A) $- \frac { 1 } { 5 }$
B)0
C) $\frac { 1 } { 5 }$
D)1
E)Does not exist

Question 67

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \ln \left( \frac { e ^ { x } } { 2 } \right)$ ?

A) $\ln 2$
B)0
C) $\ln 2$ .
D) $\frac { 1 } { 2 }$
E)Does not exist

Question 68

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { 1 - e ^ { x } } { e ^ { 2 x } }$ ?

A)-1
B)0
C)1
D) $\frac { 1 } { 2 }$
E)Does not exist

Question 69

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \sin ( 5 x ) } { \sin ( 3 x ) }$ ?

A) $- \frac { 5 } { 3 }$
B) $- \frac { 3 } { 5 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 5 } { 3 }$
E)Does not exist

Question 70

Which of the following is equal to limit $\lim _ { x \rightarrow 0 ^ { - } } - \frac { 2 x } { \sin ( 3 x ) }$ ?

A) $- \frac { 3 } { 2 }$
B) $- \frac { 2 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 3 } { 2 }$
E)Does not exist

Question 71

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { 1 - \cos ^ { 4 } x } { 5 x }$ ?

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 5 }$
C)0
D)1
E)Does not exist

Question 72

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } - 3 \sin ( 2 x ) } { 5 x }$ ?

A) $- \frac { 6 } { 5 }$
B) $- \frac { 5 } { 6 }$
C)0
D) $\frac { 5 } { 6 }$
E) $\frac { 1 } { 5 }$

Question 73

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \frac { \cos ^ { 2 } ( 3 x ) - 1 } { 5 x }$ ?

A) $- \frac { 6 } { 5 }$
B) $- \frac { 5 } { 6 }$
C)0
D) $\frac { 5 } { 6 }$
E) $\frac { 6 } { 5 }$

Question 74

Which of the following equal to limit $\lim _ { x \rightarrow 1 } \ln \left( \frac { x ^ { 4 } } { e ^ { 4 x } } \right)$ ?

A)-4
B)-1
C)1
D)4
E)Does not exist

Question 75

Which of the following is equal to limit $\lim _ { x \rightarrow 1 } \left( \frac { e ^ { x } - 1 } { x ^ { 2 } - 1 } \right)$ ?

A) $- \frac { 1 } { 2 }$
B)0
C) $\frac { 1 } { 2 }$
D) $e$
E)Does not exist

Question 76

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \left( \frac { 1 - e ^ { x } } { 1 + e ^ { 3 x } } \right)$ ?

A)-1
B)0
C)1
D) $e$
E)Does not exist

Question 77

Which of the following is equal to limit $\lim _ { x \rightarrow 0 } \left( \frac { 4 - e ^ { 2 x } } { 5 + e ^ { 3 x } } \right)$ ?

A) $\frac { 4 } { 5 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 1 } { 2 }$
D)0
E)Does not exist

Question 78

Which of the following is true for the limit $\lim _ { x \rightarrow 0 } \left( \frac { x e ^ { 2 x } } { \sin x } \right)$ ?

A)-3
B)-1
C)0
D)1
E)3

Question 79

Which of the following is true for the limit $\lim _ { x \rightarrow 0 } \frac { - 3 x ^ { 3 } + 4 \sin ( 6 x ) } { 5 x }$ ?

A) $- \frac { 4 } { 5 }$
B) $- \frac { 4 } { 5 }$ .
C) $\frac { 4 } { 5 }$
D) $\frac { 24 } { 5 }$
E)Does not exist

Question 80

Which of the following is true for the limit $\lim _ { x \rightarrow 0 } \frac { \tan ( 2 x ) } { \sec x }$ ?

A)-2
B)0
C)1
D)2
E)Does not exist