91Ó°ÊÓ

$$ \begin{aligned} &\text { If } \begin{aligned} f(x) &=a x^{2}+b, \quad x \leq 1 \\ &=b x^{2}+a x+c, \quad x>1, \end{aligned}\\\ &\text { where } b \neq 0 \text { . Find } a \text { and } c \text { such that } f(x) \text { is continuous and differentiable at } x=1 \text { . } \end{aligned} $$

$$ y=0.4\left(\cos \frac{2 x+1}{2}-\sin 0.8 x\right)^{2} $$

$$ y=\sqrt{x \sin x \sqrt{1-e^{x}}} $$

$$ \text { Differentiate } \sin ^{-1} \frac{1-x}{1+x} \text { w.r.t. } \sqrt{x} $$

Draw the graph of the function \(y=|x-1|+|x-2|\) in the interval \([0,3]\) and discuss the continuity and differentiability of the function in this interval. \\{Ans. continuous, not differentiable at \(x=1 \& 2\\}\)