Evaluate ${\lim }_{x\to 0}\frac{\sqrt{x+49}-7}{x}$.

What does direct substitution give for ${\lim }_{x\to -7}\frac{x^2+4x-21}{x^2-49}$, and what follows from it?

Evaluate ${\lim }_{x\to 0}\frac{\sqrt{x+16}-4}{x}$.

What does direct substitution give for ${\lim }_{x\to 8}\frac{x^2-4x-21}{x^2-49}$, and what follows from it?

Use the graph of $f$. Evaluate ${\lim }_{x\to 2^{-}}f(x)$.

Evaluate ${\lim }_{x\to 0}\frac{\sqrt{x+144}-12}{x}$.

Use the graph of $q$. At which value of $x$ does $q$ have a REMOVABLE discontinuity?

A table gives $q(-0.1)=-4.1$, $q(-0.01)=-4.01$, $q(-0.001)=-4.001$, $q(0.001)=-3.999$, $q(0.01)=-3.99$ and $q(0.1)=-3.9$. What does the table suggest for ${\lim }_{x\to 0}q(x)$?

Use the graph of $f$. What kind of discontinuity does $f$ have at $x=2$?

A function is defined by $u(x)=cx-3$ for $x<-4$ and by $u(x)=x^2+5$ for $x\ge -4$. What value of $c$ makes $u$ continuous at $x=-4$?

Use the graph of $f$. Evaluate ${\lim }_{x\to -3}f(x)$.

What does direct substitution give for ${\lim }_{x\to 7}\frac{x^2-11x+30}{x^2-25}$, and what follows from it?

Evaluate ${\lim }_{x\to -4}\frac{x^2+2x-8}{x+4}$.

Use the graph of $f$. Evaluate ${\lim }_{x\to 5}f(x)$.

Evaluate ${\lim }_{x\to 5}\frac{x^2+3x-40}{x-5}$.

For $r(x)=3x^2+6$, simplify $\frac{r(-2+h)-r(-2)}{h}$.

A table gives $v(-2.1)=-6.1$, $v(-2.01)=-6.01$, $v(-2.001)=-6.001$, $v(-1.999)=-5.999$, $v(-1.99)=-5.99$ and $v(-1.9)=-5.9$. What does the table suggest for ${\lim }_{x\to -2}v(x)$?

A table gives $w(-3.1)=5.9$, $w(-3.01)=5.99$, $w(-3.001)=5.999$, $w(-2.999)=6.001$, $w(-2.99)=6.01$ and $w(-2.9)=6.1$. What does the table suggest for ${\lim }_{x\to -3}w(x)$?

A table gives $w(0.9)=7.9$, $w(0.99)=7.99$, $w(0.999)=7.999$, $w(1.001)=8.001$, $w(1.01)=8.01$ and $w(1.1)=8.1$. What does the table suggest for ${\lim }_{x\to 1}w(x)$?

Use the graph of $f$. Evaluate ${\lim }_{x\to -6}f(x)$.

For $q(x)=6x^2+8$, what is $q(x+h)$ expanded?

A table gives $r(3.9)=-1.1$, $r(3.99)=-1.01$, $r(3.999)=-1.001$, $r(4.001)=-0.999$, $r(4.01)=-0.99$ and $r(4.1)=-0.9$. What does the table suggest for ${\lim }_{x\to 4}r(x)$?

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

Evaluate ${\lim }_{x\to -3}\left(-2x^2+x+1\right)$.

For $q(x)=-2x^2-5$, simplify $\frac{q(-2+h)-q(-2)}{h}$.

Simplify $\frac{v(x+h)-v(x)}{h}$ for $v(x)=\sqrt{x+8}$, leaving no $h$ standing alone in the denominator.

What does direct substitution give for ${\lim }_{x\to -2}\frac{x^2+7x+12}{x^2-16}$, and what follows from it?

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{6+h}-\frac{1}{6}}{h}$.

Use the graph of $h$. At which value of $x$ does $h$ have an INFINITE discontinuity?

A function is defined by $s(x)=cx+2$ for $x<-4$ and by $s(x)=x^2-6$ for $x\ge -4$. What value of $c$ makes $s$ continuous at $x=-4$?