If `f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n` discuss the continuity of `f(x),g(x),a n dfog(x)dot`

Discuss the continuity of f(x)={1/(e^(x-1)),x!=1 0,x=1

Discuss the continuity of f(x)=(lim)_(n->oo)(x^(2n)-1)/(x^(2n)+1)

f(x) = |x| + |x-1| at x = 1 . discuss the continuity

Let fa n dg be real functions defined by f(x)=x/(x+1)a n dg(x)=1/(x+3)dot Describe the functions gofa n dfog (if they exist).

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) is equal to (a) f(3x) (b) {f(x)}^3 (c) 3f(x) (d) -f(x)

If f,\ g,\ h are real functions defined by f=sqrt(x+1),\ g(x)=1/x\ a n d\ h(x)=2x^2-3, then find the values of (2fg+g-h)(1)\ a n d\ (2f+g-h)(1)dot

If f(x)=(sin3x)/x,w h e nx!=0, f(x)= 1,w h e n x=0 Find whether f(x) is continuous at x=0

If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n dg(x)+g(a-x)=2, then show that int_0^af(x)g(x)dx=int_0^af(x)dxdot