Evaluate the limit: $\mathop {\lim }\limits_{x \to 3} (x+3)$

The value of $\mathop {\lim }\limits_{n \to \infty } \frac{{1 + 2 + 3 + .... + n}}{{{n^2} + 100}}$ is equal to:

Let $f(x)$ be a differentiable function such that $f(0)=0$ and $f^{\prime}(0)=20$. For $x \in \left(0, \frac{\pi}{2}\right]$,if $A(x)=2 f(x) \operatorname{cosec} 4 x+4 f(x)\left(\cos ^2 x+1\right)-4 \cos ^2 x$,then $\lim _{x \rightarrow 0} A(x)=$

$\lim _{x \rightarrow \infty}\left[\sqrt{x^2+2 x-1}-x\right]$ is equal to :

$\lim _{x \rightarrow 0} \frac{a^x-1}{\sin (x)} = $

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 0} x \sec x$