1. Limits and Continuity

Determine the interval(s) for which the function is continuous.

$f\left(x\right)=x^2+4x-12$

Determine the interval(s) for which the function is continuous.

Use continuity to evaluate the limit: $\underset{x\to 1}{lim}\frac{ln(7-x^2)}{1+x}$

For what value of the constant $c$ is the function $$f\left(x\right)=\left\{\begin{array}{ll}2x+1& \text{, }x<3\\ c& \text{, }x=3\\ x^2-2& \text{, }x>3\end{array}\right\}$$ continuous on $ℝ$?

Use continuity to evaluate the limit: $\underset{x\to 2}{lim}3x^2-5x+4$.

Determine the value(s) of $x$ (if any) for which the function is discontinuous.

$f\(\left\)(x\(\right\))=\(\frac{x-4}{x^2-x-12}\)$

Use the graph of $f\(\left\)(x\(\right\))$ to determine if the function is continuous or discontinuous at $x=c$.

$c=3$

Use graph of $f\(\left\)(x\(\right\))$ to determine if the function is continuous or discontinuous at $x=c$

$c=0$

Determine the interval(s) for which the function is continuous.

$f(x)=\(\frac{sinx}{(2+cosx)}\)$

Determine the value(s) of $x$ (if any) for which the function is discontinuous.

Use the graph of $f\(\left\)(x\(\right\))$ to determine if the function is continuous or discontinuous at $x=c$.

$c=4$

Use the graph of $f\(\left\)(x\(\right\))$ to determine if the function is continuous or discontinuous at $x=c$.

$c=-2$