Infinite Limits

Practice: Trig Limits

Evaluate $\displaystyle\lim_{x\to0}\ \frac{2\sin5x}{x^2}$.

Determine $\lim_{x\ \rightarrow0}\ \ln\left(-\ln\left(x^2\right)\right)$.

Evaluate $\lim\ _{x\rightarrow2^+}\frac{x-3}{2-x}$

Evaluate $\displaystyle \lim_{x\to\infty}\arctan\left(x-x^3\right)$

🦊 TRICKY! Evaluate the limit,$\displaystyle\lim_{x\rightarrow \infty} \sqrt{x^2-10x}-x^2$ .

Determine if the function $h\left(x\right)=\frac{e^{\pi}+1}{\ln\left(3x-2\right)}$ has any vertical asymptotes.

🌶 TOUGH! Evaluate the limit,$\displaystyle\lim_{x\rightarrow 2}\frac{-5(x+1)}{x-2}$ .

Find the following limit:

Find the exact list of vertical asymptotes of

$f(x)=\frac{x^2+4x}{x^2-16}$

Determine if the function $h\left(t\right)=\frac{e^{\pi}+1}{\ln\left(3x-2\right)}$ has any vertical asymptotes.

Find the exact list of vertical asymptotes of $$$\displaystyle f(x)=\frac{x^2+4x}{x^2-16}$.

Find all asymptotes for $\displaystyle f(x)=\frac{3x^2+x+1}{x^2-1}$ . Enter as comma-separated values (no spaces in between), smaller value first

Determine $\displaystyle\lim_{x \rightarrow\pi^-}\ln(\sin x)$ .

Determine if the function $g\left(x\right)=e^{-x^2+2x-3}$ has any horizontal asymptotes.

$\bf{Q:}$ Determine if the function $f\left(x\right)=\displaystyle\frac{e^{\pi}+1}{\ln\left(3x-2\right)}$ has any vertical asymptotes.

Determine the value of $\displaystyle \lim_{t \to 2^+}\log_3 \left( \frac{1}{t-2} \right)$.

Which of the following statements is true about the function$f\left(x\right)=\frac{7x^{\frac{7}{2}}+x^{\frac{1}{2}}+1}{5x^{\frac{7}{2}}-5x^{\frac{1}{2}}}$?

Find the asymptote(s), if any, of

$\displaystyle \lim_{x\rightarrow2}\frac{(x-9)(x+2)}{x-2}$

Given the function $f(x)=\begin{cases} \arctan x+\pi/2&\text{if }x \le 0\\ \frac{2}{x}&\text{if }0<x\le e\\ \frac{1}{\ln x}&\text{if }x>e \end{cases}$, which of the following statements is true about $f(x)$?

Evaluate:

Determine if the function $g\left(x\right)=e^{-x^2+2x-3}$ has any horizontal asymptotes.

Find the exact list of vertical asymptotes of $$$\displaystyle f(x)=\frac{x^2+4x}{x^2-16}$.

Find all asymptotes for $\displaystyle f(x)=\frac{3x^2+x+1}{x^2-1}$ . Enter as comma-separated values (no spaces in between), smaller value first

Determine $\displaystyle\lim_{x \rightarrow\pi^-}\ln(\sin x)$ .

$\bf{Q:}$ Determine if the function $f\left(x\right)=\displaystyle\frac{e^{\pi}+1}{\ln\left(3x-2\right)}$ has any vertical asymptotes.

Determine $\lim_{x\ \rightarrow0}\ \ln\left(-\ln\left(x^2\right)\right)$.

Practice: Trig Limits

Evaluate $\displaystyle\lim_{x\to0}\ \frac{2\sin5x}{x^2}$.

Evaluate $\lim\ _{x\rightarrow2^+}\frac{x-3}{2-x}$

Evaluate $\lim\ _{x\rightarrow2^+}\frac{x-3}{2-x}$

Practice: Trig Limits

Evaluate $\displaystyle\lim_{x\to0}\ \frac{2\sin5x}{x^2}$.

Which of the following statements is true about the function$f\left(x\right)=\frac{7x^{\frac{7}{2}}+x^{\frac{1}{2}}+1}{5x^{\frac{7}{2}}-5x^{\frac{1}{2}}}$?

Determine if the function $g\left(x\right)=e^{-x^2+2x-3}$ has any horizontal asymptotes.

Which of the following statements is true about the function$f\left(x\right)=\frac{7x^{\frac{7}{2}}+x^{\frac{1}{2}}+1}{5x^{\frac{7}{2}}-5x^{\frac{1}{2}}}$?

Evaluate $\lim\ _{x\rightarrow2^+}\frac{x-3}{2-x}$

Determine $\lim_{x\ \rightarrow0}\ \ln\left(-\ln\left(x^2\right)\right)$.

Determine $\lim_{x\ \rightarrow0}\ \ln\left(-\ln\left(x^2\right)\right)$.

Which of the following statements is true about the function$f\left(x\right)=\frac{7x^{\frac{7}{2}}+x^{\frac{1}{2}}+1}{5x^{\frac{7}{2}}-5x^{\frac{1}{2}}}$?

Which of the following statements is true about the function$f\left(x\right)=\frac{7x^{\frac{7}{2}}+x^{\frac{1}{2}}+1}{5x^{\frac{7}{2}}-5x^{\frac{1}{2}}}$?

Determine $\lim_{x\ \rightarrow0}\ \ln\left(-\ln\left(x^2\right)\right)$.

Determine $\displaystyle\lim_{x \rightarrow\pi^-}\ln(\sin x)$ .

Evaluate $\displaystyle \lim_{x\to\infty}\arctan\left(x-x^3\right)$

Evaluate $\displaystyle \lim_{x\to\infty}\arctan\left(x-x^3\right)$

Determine if the function $g\left(x\right)=e^{-x^2+2x-3}$ has any horizontal asymptotes.

Find the following limit: