# Recent questions in Limits and continuity

Limits and continuity

### Find the limits $$\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]$$

Limits and continuity

### Find the following limit: $$\lim_{(x,y)\rightarrow(3,3)}(\frac{x-y}{\sqrt x-\sqrt y})$$

Limits and continuity

### Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(1,0)}\frac{y\ln y}{x}$$

Limits and continuity

### Find the limits: $$\lim_{t\rightarrow1}\frac{t^2+t-2}{t^2-1}$$

Limits and continuity

### Evaluate the following limits. $$\lim_{x\rightarrow0}\frac{\tan7x}{\sin x}$$

Limits and continuity

### Evaluate the following limits. $$\lim_{x\rightarrow-3}\frac{\sin(x+3)}{x^2+8x+15}$$

Limits and continuity

### Find the limits $$\lim_{x\rightarrow0}\frac{\sin x}{2x^2-x}$$

Limits and continuity

### Find the following limit. $$\lim_{x\rightarrow+\infty}(\frac{3-12x}{3x+5}+\csc\frac{\pi x+\pi}{4x})$$

Limits and continuity

### Find the limits. $$\lim_{x\rightarrow3\sqrt2}(\frac{x}{2}-\frac{1}{x})$$

Limits and continuity

### Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(1,0)}\frac{\sin xy}{xy}$$

Limits and continuity

### Evaluate the following limits. $$\lim_{x\rightarrow\infty}(3\cdot2^{1-x}+x^2\cdot2^{1-x})$$

Limits and continuity

### Find the limits. $$\lim_{x\rightarrow\infty}\frac{e^{x^2}}{xe^x}$$

Limits and continuity

### Evaluate the following limits. $$\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{x^2+xy-xz-yz}{x-z}$$

Limits and continuity

### Find the limit: $$\lim_{t\rightarrow\infty}e^{3t}\sin^{-1}\frac{1}{t}$$

Limits and continuity

### A piecewise function is given. Use properties of limits to find the shown indicated limit, or state that the limit does not exist. $$f(x)=\begin{cases}\sqrt[3]{x^2+7}&\text{if}&x<1\\4x&\text{if}&x\geq1\end{cases}$$ $$\lim_{x\rightarrow1} f(x)$$

Limits and continuity

### Find the following complex limits. $$\lim_{n\rightarrow\infty}\frac{1}{3+ni}$$

Limits and continuity

### Find the following complex limits. $$\lim_{n\rightarrow\infty}\frac{6n}{2n-n^2i}$$

Limits and continuity

### Find the limit $$\lim_{b\rightarrow1^-}\int_0^b\frac{dx}{\sqrt{1-x^2}}$$

Limits and continuity