# Recent questions in Limits and continuity

Limits and continuity

### Use L'Hospital Rule to find the limits $$\lim_{x\rightarrow0}\frac{\sin mx}{\sin nx}$$

Limits and continuity

### Use Taylor's theorem to evaluate the following limits. $$\lim_{x\rightarrow0}\frac{x\sin(x)-x^2}{\cos(x)-1+\frac{x^2}{2}}$$

Limits and continuity

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

Limits and continuity

### Find the limits $$\lim_{x\rightarrow-3}\frac{2-\sqrt{x^2-5}}{x+3}$$

Limits and continuity

### Determine the limits if they exist: $$\lim_{(x,y)\rightarrow(2,4)}\frac{(x-2)^2(y-4)^2}{(x-2)^3+(y-4)^3}$$

Limits and continuity