Limits and Cont...

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

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 4}\dfrac{2-\sqrt{x}}{4-x}$$.

Evaluate the following limits.
If $$\displaystyle\lim_{x\rightarrow a}\dfrac{x^9-a^9}{x-a}=9$$, find all possible values of a.

Evaluate the following limits.
If $$\displaystyle\lim_{x\rightarrow a}\dfrac{x^5-a^5}{x-a}=405$$, find all possible values of a.

Evaluate the following limits.
$$\displaystyle\lim_{x\rightarrow 2}\dfrac{\sqrt{1+4x}-\sqrt{5+2x}}{x-2}$$.

Evaluate the following limit.
$$\displaystyle\lim_{x\rightarrow 0}\dfrac{8^x-2^x}{x}$$.

If $$f : R \rightarrow (0, \infty)$$ is an increasing function and if $$\displaystyle\lim_{x \rightarrow 2018} \dfrac{f(3x)}{f(x)} = 1$$, then $$\displaystyle\lim_{x \rightarrow 2018} \dfrac{f(2x)}{f(x)}$$ is equal to 

If $$f$$ is differentiable at $$x = 1$$ and $$\underset{h \rightarrow 0}{\lim} \dfrac{1}{h} f (1 + h) = 5, f'(1) = $$

$$\displaystyle \lim _{x \rightarrow 0} \dfrac{x\left(e^{x}-1\right)}{1-\cos x} $$ is equal to

$$ \displaystyle \lim _{x \rightarrow-\infty} \dfrac{x^{2} \tan \dfrac{1}{x}}{\sqrt{8 x^{2}+7 x+1}} $$ is equal to