Let $f(x)=\frac{e^x-e^{-x}}{2}, x \in R$. Let $f^{(k)}(a)$ denote the $k^{\text {th }}$ derivative of $f$ evaluated at $a$. What is the value of $f^{(10)}(0)$ ?(Note: ! denotes factorial)

Consider two functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow(1, \infty)$. Both functions are differentiable at a point c . Which of the following functions is/are ALWAYS differentiable at c ? The symbol $\cdot$ denotes product and the symbol odenotes composition of functions.

$$\mathop {\lim }\limits_{t \to + \infty } \sqrt{t^2+t}-t= $$

(Round

off to one decimal place)