$\lim\limits_{x\to0}\left(\tan\left({\pi\over4}+x\right)\right)^{1/x}$ is equal to (1) 2 (2) 1 (3) e (4) e2

$\lim\limits_{y\to0} {\sqrt{1+\sqrt{1+y^4}}-\sqrt2\over y^4}$ (1) exists and equals $1\over4\sqrt2$ (2) does not exist (3) exists and equals $1\over2\sqrt2$ (4) exists and equals $1\over2\sqrt2(\sqrt2+1)$

Let $f:R\to R$ be a function defined as : $f(x)=\begin{cases}5,&\text{if}&x\leq1\\a+bx,&\text{if}&1<x<3\\b+5x,&\text{if}&3\leq x<5\\30,&\text{if}&x\geq5\end{cases}$ Then, $f$ is : (1) continuous if $a=5$ and $b=5$ (2) continuous if $a=-5$ and $b=10$ (3) ...

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