1. Limits and Continuity

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

Use the continuity of the absolute value function (Exercise 78) to determine the interval(s) on which the following functions are continuous.

$g\left(x\right)=\mid \frac{x+4}{x^2-4}\mid$

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: $\underset{x\to 2}{lim}3x^2-5x+4$.

Limits of quotients

Find the limits in Exercises 23–42.

limu→1 (u⁴ − 1)/(u³ − 1)

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

$c=0$

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

$c=-2$

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

$c=3$

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

$c=4$

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

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

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

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.

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

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

Suppose f(x) = {x^2 − 5x + 6 / x − 3 if x≠3

a if x=3.

Determine a value of the constant a for which lim x→3 f(x) = f(3).