Let `f(x)={x/2-1,0lt=xlt=1 1/2,1lt=xlt=2}g(x)=(2x+1)(x-k)+3,0<=x<=oo then g(f(x))` is continuous at x=1 if k equal to:

Evaluate the following integrals: int_0^9f(x)dx ,w h e r ef(x)={sinx,0 lt=xlt=pi//2 1,pi/2lt=xlt=3 e^(x-3),3lt=xlt=9

If f(x)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x >0 f(x)={1/(64),0lt=xlt=1/4x^2,1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

If f(x)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x >0 f(x)={1/(64),0lt=xlt=1/4x^2,1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Evaluate the following integral: int_0^9f(x)dx ,\ w h e r e\ f(x){sinx ,\ 0lt=xlt=pi//2 1,pi/2lt=xlt=3e^(x-3),\ 3lt=xlt=9

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

If f(x)=max{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x > 0 f(x) = { 1/(64), 0 lt= x lt = 1/4 x^2, 1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

If f(x)=max{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x > 0 f(x) = { 1/(64), 0 lt= x lt = 1/4 x^2, 1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

Discuss the applicability of Rolles theorem on the function f(x)={(x^2+1 ,, if \ 0lt=xlt=1),(3-x ,,if 1ltxlt=2):}