[" If the function "g(x)=],[{[k sqrt(x+1),quad 0quad <=x<=],[mx+2quad ,3

If the function,g(x)={k sqrt(x+1),0<=x<=3mx+2,3

For what value of k is the function f(x)={(sin2x)/(x),quad x!=0k,quad x=0 continuous at x=0?

Discuss the continuity of the function f(x)={x,quad x>01,quad x=0-x,quad x<0 at the point x=0 .

Discuss the continuity of the function f(x)={(|x|)/(x)quad ,quad if quad x!=00quad ,quad if x=0

Discuss the continuity of the function f(x)={(x)/(|x|)quad ,quad x!=00quad ,quad x=0

Determine the value of the constant k so that the function f(x)={(sin2x)/(5x),quad if x!=0k,quad if x=0 is continuous at x=0

Prove that the function f(x)={(x)/(|x|+2x^(2)),quad x!=0k,quad x=0 remains discontinuous at x=0, regardless the choice of k.

For what value of k is the function f(x)={(x^(2)-1)/(x-1),quad x!=1k,quad x=1 continuous at x=1?

Show that the function f(x)={x^(m)sin((1)/(x)),quad x!=00,quad x= is differentiable at x=0, if m>1