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`

Find the values of aa n db if f(x)={a+sin^(-1)(x+b), xgeq1 and x ,x<1 is differentiable at x=1.

The function f(x) = {{:(2, x lt=1),(x , x gt 1 ):} is not differentiable at ………..

Find the values of aa n db such that int(dx)/(1+sinx)=tan(x/2+a)+b

If f(x)={x ,xlt=1,x^2+b x+c ,x >1' find b and c if function is continuous and differentiable at x=1

Find lim_(x to 1) f(x) if f(x)={:{(x^2-1,x le1),(x^2+1, x gt1):}

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xgt1

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

Show that f(x)=x^(2) is differentiable at x=1 and find f'(1) .

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