# Recent questions in Limits and continuity

Limits and continuity

### Find the limits $$\lim_{y\rightarrow2}\frac{y+2}{y^2+5y+6}$$

Limits and continuity

### Evaluate the following limit. If you use L'Hospital Rule, be sure to indicate when you are using it, and why it applies. $$\lim_{x\rightarrow\infty}(3\cdot2^{1-x}+x^2\cdot2^{1-x})$$

Limits and continuity

### Find the limits: $$\lim_{x\rightarrow\infty}(\sqrt{x+9}-\sqrt{x+4})$$

Limits and continuity

### Find the limits. $$\lim_{x\rightarrow-\infty}\frac{2^x+4^x}{5^x-2^x}$$

Limits and continuity

### Find the limit $$\lim_{u\rightarrow1}\frac{u^4-1}{u^3-1}$$

Limits and continuity

### Find the limits: $$\lim_{x\rightarrow4}\frac{4x-x^2}{2-\sqrt{x}}$$

Limits and continuity

### Find the following complex limits. $$\lim_{n\rightarrow\infty}\frac{2n}{7n+ni}$$

Limits and continuity

### Evaluate the following limits. $$\lim_{(x,y)\rightarrow(1,-1)}\frac{10uv-2v^2}{u^2+v^2}$$

Limits and continuity

### Evaluate the following limits or determine that they do not exist. $$\lim_{(x,y,z)\rightarrow(2,2,3)}\frac{x^2z-3x^2-y^2z+3y^2}{xz-3x-yz+3y}$$

Limits and continuity

### Use L'Hospital Rule to evaluate the following limits. $$\lim_{x\rightarrow0}\frac{\tanh^{-1}x}{\tan(\pi x/2)}$$

Limits and continuity

### Evaluate the limit: $$\lim_{x\rightarrow\infty}\frac{e^x}{x^4}$$

Limits and continuity

### Evaluate the limit $$\lim_{x\rightarrow\infty}\frac{4x^3-2}{3x^4+5x}$$

Limits and continuity

### Evaluate the following limits. $$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}$$

Limits and continuity

### Evaluate the following limit. $$\lim_{x\rightarrow0^+}(1+5x)^{2/x}$$

Limits and continuity

### Use L'Hospital Rule to evaluate the following limits. $$\lim_{x\rightarrow0}(\tanh x)^x$$

Limits and continuity

### Evaluate the following limits. $$\lim_{(x,y,z)\rightarrow(1,-1,1)}\frac{xz+5x+yz+5y}{x+y}$$

Limits and continuity

### Use the method of your choice to evaluate the following limits. $$\lim_{(x,y)\rightarrow(0,\pi/2)}\frac{1-\cos xy}{4x^2y^3}$$

Limits and continuity

### Use Taylor series to evaluate the following limits. $$\lim_{x\rightarrow0}\frac{\sqrt{1+2x}-1-x}{x^2}$$

Limits and continuity