Evaluate ${\lim }_{x\to 0}\frac{\sin \left(9x\right)}{5x}$, with $x$ in radians.

The table gives values of $w$ near $x=0$. Which value best estimates ${\lim }_{x\to 0}w(x)$?

Let $f(x)=x^3+x-22$, which is continuous everywhere. On which interval does the Intermediate Value Theorem guarantee a solution of $f(x)=0$?

Evaluate ${\lim }_{x\to \infty }\frac{8x^2+9x}{-7x^2+9}$.

Let $w(x)=\{\begin{array}{ll}4x+k& x<-3\\ x^2+4& x\ge -3\end{array}$. For what value of $k$ is $w$ continuous at $x=-3$?

Evaluate ${\lim }_{x\to -5^{-}}\frac{x+4}{x+5}$.

Let $u(x)=\{\begin{array}{ll}4x-8& x\le 4\\ 2x& x>4\end{array}$. Which statement about ${\lim }_{x\to 4}u(x)$ is correct?

Evaluate ${\lim }_{x\to 3}\frac{x^2-8x+15}{x^2-7x+12}$.

Evaluate ${\lim }_{x\to 5^{-}}\frac{x+5}{x-5}$.

Evaluate ${\lim }_{x\to -2^{+}}\frac{x-4}{x+2}$.

Evaluate ${\lim }_{x\to \infty }\frac{-6x+1}{x^2-7}$.

Evaluate ${\lim }_{x\to \infty }\frac{x+7}{x^2+1}$.

Evaluate ${\lim }_{x\to -7}\frac{x^2-49}{x+7}$.

Let $r(x)=\frac{x^2+2x-8}{x+4}$. Which condition for continuity at $x=-4$ fails?

Let $f(x)=\{\begin{array}{ll}3x+k& x<-1\\ x^2+4& x\ge -1\end{array}$. For what value of $k$ is $f$ continuous at $x=-1$?

Classify the discontinuity of $q(x)=\frac{x-8}{x+2}$ at $x=8$.

Evaluate ${\lim }_{x\to -6}\frac{x^2+10x+24}{x^2-36}$.

Let $v(x)=\frac{x^2-x-30}{x-6}$. Which condition for continuity at $x=6$ fails?

Evaluate ${\lim }_{x\to 6}\frac{x^2-8x+12}{x^2-2x-24}$.

Let $r(x)=\{\begin{array}{ll}x-4& x\le -4\\ 2x& x>-4\end{array}$. Which statement about ${\lim }_{x\to -4}r(x)$ is correct?

Let $f(x)=x^3+x-14$, which is continuous everywhere. On which interval does the Intermediate Value Theorem guarantee a solution of $f(x)=0$?

The figure shows the graph of $f$. What is ${\lim }_{x\to 2^{-}}f(x)$?

At which value of $x$ does $q(x)=\frac{(x-5)(x-2)}{(x-5)(x+5)}$ have a REMOVABLE discontinuity?

The figure shows the graph of $w$. What is ${\lim }_{x\to 3}w(x)$?

Evaluate ${\lim }_{x\to \infty }\frac{3x-2}{x^2-3}$.

Let $p(x)=\{\begin{array}{ll}-3x+4& x<0\\ x^2+9& x\ge 0\end{array}$. Evaluate ${\lim }_{x\to 0^{+}}p(x)$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(5x\right)}{2x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to 8}\frac{x^2-64}{x-8}$.

Suppose $-x^2-15\le r(x)\le 6x-7$ for all $x$ near $-2$. What is ${\lim }_{x\to -2}r(x)$?

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(7x\right)}{5x}$, with $x$ in radians.

The table gives values of $v$ near $x=-4$. Which value best estimates ${\lim }_{x\to -4}v(x)$?

Evaluate ${\lim }_{x\to \infty }\frac{-7x^2+2x}{9x^2+2}$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(2x\right)}{6x}$, with $x$ in radians.

The figure shows the graph of $f$. What is ${\lim }_{x\to -3}f(x)$?

The figure shows the graph of $s$. What is ${\lim }_{x\to -3^{+}}s(x)$?

Let $u(x)=\{\begin{array}{ll}-3x+3& x<2\\ x^2+9& x\ge 2\end{array}$. Evaluate ${\lim }_{x\to 2^{-}}u(x)$.

Evaluate ${\lim }_{x\to 0}\frac{\sin \left(6x\right)}{7x}$, with $x$ in radians.

Evaluate ${\lim }_{x\to \infty }\frac{-x^2+x}{-8x^2+1}$.

Evaluate ${\lim }_{x\to -5}\frac{x^2-25}{x+5}$.

Evaluate ${\lim }_{x\to -4^{-}}\frac{x-1}{x+4}$.