" 13.Letf "(x)={[1+x,,0<=x<=20],[3-x,,2

Letf(x)= x^2+b_1x+c_1 ,g(x)= x^2+b_2x+c_2 . Real roots fo f(x)=0 be alpha,beta and real roots ofg(x)=0 be alpha+delta,beta+delta .Least value of f(x) be -1/4. Least value of g(x) occurs at x=7/2 The least value of g(x) is

If f(x)={{:(-1, x lt 0),(0, x=0 and g(x)=x(1-x^(2))", then"),(1, x gt 0):}

If f(x)={{:(-1, x lt 0),(0, x=0 and g(x)=x(1-x^(2))", then"),(1, x gt 0):}

Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,x=0]:} at x=0.

The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0 \ \ \ \ \ \ \ 0,x=0 at x=0

Show that the function f(x)={x^msin(1/x), x=0 ,0 ,\ \ \ x!=0 ,\ \ \ \ \ \ \x=0 is differentiable at x=0 , if m >1

Check the continuity of f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):}at x = 0

If f(x) = {(x-1,",", x lt 0),(1/4,",",x = 0),(x^2,",",x gt 0):}

If f(x) = {(x-1,",", x lt 0),(1/4,",",x = 0),(x^2,",",x gt 0):}