Find the equivalent definition of `f(x)=max{x^2,(1-x)^2,2x(1-x)}`where `0lt=xlt=1`

Discuss the differentiability of f(x)="max"{x^2-3x+2,2-|x-1|}

Draw the graph of the function f(x)=max dot {(sinx ,cos2x)},x in [0,2pi]dot Write the equivalent definition of f(x) and find the range of the function.

Consider the function f(x)={2x+3,xlt=1 -x^2+6,x >1

Let f(x) =M a xi mu m {x^2,(1-x)^2,2x(1-x)}, where 0lt=xlt=1. Determine the area of the region bounded by the curves y=f(x) ,x-axis ,x=0, and x=1.

Find the limits lim_ (x to 1) f(x) where f(x)={:{(x^2+2,x ne1),(1,x=1):}

Find the value of "cos"(2cos^(-1)x+sin^(-1)x) at x=1/5, where 0lt=pi and -pi/2lt=sin^(-1)xlt=pi/2dot

Find the maxima and minima of the function y=x(x-1)^2,0lt=xlt=2.

The probability density function of X is f(x) = {(x,0 ltxlt1),(2-x, 1lt=xlt2),(0,"otherwise"):} Find (i) P(0.2 lt=X lt0.6) (ii) P(1.2lt= X lt 1.8) (iii) P(0.5 lt=X lt 1.5)

Find the values of aa n db if f(x)={a x^2+1,xlt=1 ,x^2+a x+b ,x >1"i s differentiable at"x=1

Consider the function f(x)={{:(x-[x]-(1)/(2),x !in),(0, "x inI):} where [.] denotes the fractional integral function and I is the set of integers. Then find g(x)max.[x^(2),f(x),|x|},-2lexle2.