Exam 2: Limits and Continuity

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 $\lim _ { x \rightarrow 1 } f ( x )$ ?

Let $f ( x ) = \frac { 2 x - 1 } { 2 x ^ { 2 } + 5 x - 3 }$ The set of all vertical asymptotes of ƒ is

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 $\lim _ { x \rightarrow - 1 } f ( x )$ ?

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

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

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

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

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

Consider $\lim _ { x \rightarrow - 1 } 2 x = - 2$ In order for $| 2 x - ( - 2 ) | < 0.01$ whenever $0 < | x + 1 | < \delta$ which of the following is true for the largest ??

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

The limit $\lim _ { x \rightarrow \infty } \frac { 3 - x ^ { 2 } } { - 2 x + 1 }$ is

The limit $\lim _ { x \rightarrow 4 ^ { - } } \frac { 2 x } { 2 x ^ { 2 } - 9 x + 4 }$ is

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

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

Let $f ( x ) = \frac { \lfloor x + 1 \rfloor } { x + 1 }$ . The set of all vertical asymptotes of ƒ is

Let $f ( x ) = \frac { - 4 x ^ { 2 } } { x + 6 }$ The set of all horizontal asymptotes of ƒ is

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

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

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

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