Amit M Agarwal Solutions for Chapter: Graphical Transformations, Exercise 2: Proficiency in 'Graphical Transformations' Exercise 2

Find the area enclosed by the curves: $\max \left(\right|x|, |y\left|\right)=1$.

Find the area enclosed by the curves:  $\max \left(\right|2x|, |2y\left|\right)=1$.

Find the area enclosed by the curves: max$\left(\right|x+y|, |x-y\left|\right)=1$.

Find the area enclosed by $|x+y-1|+|2x+y+1|=1$.

Find $f\left(x\right)$ when it is given by $f\left(x\right)=\max \left\{x^3,x^2,\frac{1}{64}\right\}$, $\forall x\in [0,\infty )$.

Find the number of solutions of $2^{\left|x\right|}=\sin x^2$.

Find the number of solutions of $\sin x=x^2+x+1$.

Find the number of solutions of $\sin \pi x=\left|\log \right|x\left|\right|.$