Limits and Cont...

Which of the following statement is not correct

What is the value of $$\underset{x\rightarrow 0}{lim}\dfrac{\sin\,x}{\tan \,3x}$$

If $$f(x)=\left\{\begin{array}{l}x-5;\>x\leq 1\\4x^{2}-9;\>1<x\le2\\3x^{2}+4;\>x>2\end{array}\right.$$
Then $$f(2^{+})-f(2^{-})=$$

 If $$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}2\mathrm{x}+\mathrm{b}(\mathrm{x}<\alpha)\\\mathrm{x}+\mathrm{d}(\mathrm{x}\geq\alpha)\end{array}\right.$$is such that
$$\displaystyle \lim_{x\rightarrow \alpha}f(x) =L$$, then $$L=$$

lf $$f(x)=x,x<0;f(x)=0,x=0$$; $$f(x)=x^{2};x>0$$, then $$\displaystyle \lim_{x\rightarrow 0}f(x)$$ is equal to

$$f(x)=2x+1, a=1,l=3$$ and $$\epsilon=0.001$$, then $$\delta>0$$ satisfying $$0<|x-a|<\delta$$ such that $$|f(x)-l|<\epsilon$$, is

 Evaluate: $$\displaystyle \lim_{h\rightarrow 0}\left(\frac{1}{h\sqrt[3]{8+h}}-\frac{1}{2h}\right)$$

$$\displaystyle \lim_{x\rightarrow 0}\frac{(1-e^{x})\sin x}{x^{2}+x^{3}}=$$

 lf $$\displaystyle \lim_{x\rightarrow a^+}f(x)=L$$, then for each $$\epsilon>0$$, there exists $$\delta>0$$ so that

$$\displaystyle \lim_{x\rightarrow 0}\frac{1-\cos x}{x\log(1+x)}=$$