Exam 2: Limits and Continuity

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 $\lim _ { x \rightarrow - 2 } f ( x )$ ?

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

Which of the following is true for the limit $\lim _ { x \rightarrow 0 } \frac { 1 - \cos ^ { 2 } x } { 3 x }$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Consider $\lim _ { x \rightarrow - 3 } ( | x | + 1 ) = 4$ In order for $| ( | x | + 1 ) - 4 | < 0.01$ whenever $0 < | x - ( - 3 ) | < \delta$ which of the following is true for the largest ?

Let $f ( x ) = \frac { | x | } { x }$ The set of all vertical asymptotes of ƒ is