`s g n(x^2-1)=(x+1)^2`

Show that 1/(x+1)+2/(x^2+1)+4/x^4+1)+…..+2^n/(x^2^n+1)= /(x-1)- 2^(n+1)/(x^2(n+1) -1)

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

If S_(n)=(x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+y^(2)x+y^(3))+…n terms then prove that (x-y)S_(n)=[(x^(2)(x^(n)-1))/(x-1)-(y^(2)y^(n)-1)/(y-1)] .

An equation of the form (f(x))^((1)/(2n))=g(x) equivalent to the system g(x)>=0;f(x)=g^(2n)(x)

If g(x) = 1/x^2 , show that , g(x) - g(x + 1) = (2x + 1)/(x^2 (x + 1)^2) .

Let f(x) and g(x) be two continuous function and h(x)= lim_(n to oo) (x^(2n).f(x)+x^(2m).g(x))/((x^(2n)+1)). if the limit of h(x) exists at x=1, then one root of f(x)-g(x) =0 is _____.

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Which of the following functions is/are discontinuous at x=1? f(x)=1/(1+2^(t a n x)) g(x)=(lim)_(xvecoo)1/(1+n in s^2(pix)) h(x)=2^-2^(((1/(1-x)))),x!=1a n dh(1)=1 varphi(x)=(x-1)/(|x-1|+2(x-1)^2),x!=1a n dvarphi(1)=1

Which of the following functions is/are discontinuous at x=1? f(x)=1/(1+2^(t a n x)) g(x)=(lim)_(xvecoo)1/(1+n in s^2(pix)) h(x)=2^-2^(((1/(1-x)))),x!=1a n dh(1)=1 varphi(x)=(x-1)/(|x-1|+2(x-1)^2),x!=1a n dvarphi(1)=1