Limits and Cont...

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow a}\dfrac{\sqrt{x}+\sqrt{a}}{x+a}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{3x+1}{x+3}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{x^{2/3}-9}{x-27}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 1}\dfrac{\sqrt{x^2-1}+\sqrt{x-1}}{\sqrt{x^2-1}}, x > 1$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{ax+b}{cx+d}, d\neq 0$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{\sqrt{a^2+x^2}-a}{x^2}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{2x}{\sqrt{a+x}-\sqrt{a-x}}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{\sqrt{a+x}-\sqrt{a}}{x\sqrt{a^2+ax}}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 2}\dfrac{x-2}{\sqrt{x}-\sqrt{2}}$$.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow a}\dfrac{x-a}{\sqrt{x}-\sqrt{a}}$$.