Exam 2: Limits and Continuity

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 $\lim _ { x \rightarrow - 4 } f ( x )$ ?

Consider $\lim _ { x\rightarrow 5} ( 5 | x | + 5 ) = 35$ . In order for $| ( 5 | x | + 5 ) - 35 | < 0.01$ whenever $0 < | x - 6 | <\delta$ , which of the following is true for the largest ?

Consider $\lim _ { x \rightarrow 4 } ( \pi + e ) = \pi + e$ In order for $| ( \pi + e ) - ( \pi + e ) | < 0.01$ whenever $0 < | x - 0 | < \delta$ , which of the following is true for the largest ?

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

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

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

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

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

Let $f ( x ) = \frac { 3 x ^ { 2 } - 4 } { 2 x ^ { 2 } - 1 }$ The set of all horizontal asymptotes of ƒ is

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

Consider $\lim _ { x \rightarrow 4 } \left( \frac { x } { 2 } + 5 \right) = 7$ In order for $\left| \left( \frac { x } { 2 } + 5 \right) - 7 \right| < 0.01$ whenever $0 < \mid x - 4 \mid < \delta$ which of the following is true for the largest ??

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

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

Consider $\lim _ { x \rightarrow 3 } ( 4 x - 18 ) = - 6$ In order for whenever $| ( 4 x - 18 ) - ( - 6 ) | < 0.01$ which of the following is true for the largest

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

Consider $\lim _ { x \rightarrow 0 } \pi = \pi$ In order for $| \pi - \pi | < 0.01$ whenever $0 < | x - 0 | < \delta$ which of the following is true for the largest ?

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 $\lim _ { x \rightarrow 0 } f ( x )$ ?

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

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

Consider $\lim _ { x \rightarrow x } \cos ( x - \pi ) = 1$ In order for $| \cos ( x - \pi ) - 1 | < 0.01$ whenever $0 < | x - \pi | < \delta$ , which of the following is the largest ? of those listed for which this is true?