Limits and Cont...

The value of $$f(0)$$ so that the function
$$f(x)=\dfrac{\displaystyle \log\left(1+\dfrac{x}{a}\right)-\log\left(\begin{array}{l}1-\dfrac{x}{b}\end{array}\right)}{x}, (x\neq 0)$$ is continuous at $$x = 0$$ is :

The value of $$\mathrm{f}(\mathrm{0})$$ for the function $$\mathrm{f}({x})=\displaystyle \frac{2-\sqrt{(x+4)}}{\sin 2x}, x\ne 0$$ is continuous at $${x}=0$$ is

lf $$f(x)=\left\{\begin{array}{l}\dfrac{1-\sqrt{2}\sin x}{\pi-4x}  x\neq\frac{\pi}{4}\\a,x=\frac{\pi}{4}\end{array}\right.$$ is continuous at $$x=\displaystyle \frac{\pi}{4}$$ then $$a=$$

If $$ \displaystyle f(x)=\left\{\begin{array}{ll}\dfrac{\sqrt{1+kx}-\sqrt{1-x}}{x} & \mathrm{f}\mathrm{o}\mathrm{r}-\mathrm{l} \leq x<0\\2x^{2}+3x-2 & \mathrm{f}\mathrm{o}\mathrm{r} 0\leq x\leq 1\end{array}\right.$$ is continuous at $$x = 0$$ then $$k$$ is:

$$f(x)=\begin{cases}\dfrac{x^{3}+x^{2}-16x+20}{(x-2)^{2}} & if\  x\neq 2\\ k & if\  x=2\end{cases}$$
$$\mathrm{f}({x})$$ is continuous at $${x}=2$$ then $$f(2)=$$

$$f(x)=\dfrac{p+q^{\frac{1}{x}}}{r+s^{\frac{1}{x}}},
s<1, q<1,r\neq 0, \mathrm{f}(\mathrm{0})=1$$, is left continuous at $$x =0$$ then

lf $$f$$ : $$R\rightarrow R$$ is defined by $$f(x)=\left\{\begin{array}{ll}\displaystyle \frac{\cos 3x-\cos x}{x^{2}} & \mathrm{f}\mathrm{o}\mathrm{r} x\neq 0\\\lambda & \mathrm{f}\mathrm{o}\mathrm{r} x=0\end{array}\right.$$and if $$\mathrm{f}$$ is continuous at $${x}=0$$ then $$\lambda=$$

lf $$f(x)=\displaystyle \frac{x(e^{1/x}-e^{-1/x})}{e^{1/x}+e^{-1/x}} x\neq 0$$ is continuous at $${x}=0$$, then $${f}(\mathrm{0})=$$

If $$f$$ : $$R\rightarrow R$$ is defined by $$f(x)=\left\{\begin{array}{ll}\dfrac{x+2}{x^{2}+3x+2} & x\in R-\{-1,-2\}\\-1 &  x=-2\\0 & x=-1\end{array}\right.$$then $$f$$ is continuous on the set:

If $$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}\mathrm{a}^{2}\cos^{2}\mathrm{x}+\mathrm{b}^{2}\sin^{2}\mathrm{x},\mathrm{x}\leq 0\\\mathrm{e}^{\mathrm{a}\mathrm{x}+\mathrm{b}},\mathrm{x}>0\end{array}\right.$$ is continuous at $$\mathrm{x}=0$$ then