e) Slope of the curve \( y=\sqrt{x} \) at \( (1,1) \) \( \begin{array}{ll}\text { i) } 0 & \text { ii) } 1 \\ \text { iii) }-1 & \text {-iv) } 1 / 2\end{array} \)

OR Prove that \( y \frac{d y}{d x}+x=0 \) if \( x=\frac{1-t^{2}}{1+t^{2}} \quad y=\frac{2 t}{1+t^{2}} \) Determine whether the given function ?

Cos \( \mathrm{x}=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\frac{x^{6}}{6!}+\ldots \ldots \) Show that \( \mathrm{y}=\frac{\ln x}{x} \) has maximum value at \( \mathrm{x}=\mathrm{e} \)

If \( y=\sqrt{x}-\frac{1}{\sqrt{x}} \quad \) prove that \( 2 x \frac{d y}{d x}+y=2 \sqrt{x} \)

Evaluate \( \lim _{x \rightarrow 0^{-}} \frac{5 x-4|x|}{3 x} \)

Given \( f(x)=5 x-9 \), then find \( \frac{F(2+h)-F(2)}{h} \)