" If "f(x)=(x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+(x^(2))/((1+x^(2))^(3))+...oo." Is "f(x)" continuous at origin? "

f(x)=(x^(2))/(1+x^(2))+(x^(2))/((1+x^(2))^(2))+(x^(2))/((1+x^(2))^(3))+............oo is f(x) continuous at the origin? Give reasons for your answer.

If 2f(x^(2))+3f((1)/(x^(2)))=x^(2)-1, then f(x^(2)) is

If f(x)=(x^(2))/(1+x^(2)), prove that lim_(x rarr oo)f(x)=1

Statement 1: lim_ (x rarr oo) ((1 ^ (2)) / (x ^ (3)) + (2 ^ (2)) / (x ^ (3)) + (3 ^ (2)) / (x ^ (3)) + ...... + (x ^ (2)) / (x ^ (3))) = lim_ (x rarr oo) (1 ^ (2)) / (x ^ ( 3)) + lim_ (x rarr oo) (2 ^ (2)) / (x ^ (3)) + ...... + lim_ (x rarr a) (x ^ (2)) / (x ^ (3)) lim_ (x rarr a) (f_ (1) (x) + f_ (2) (x) + ... + f_ (n) (x)) = lim_ (x rarr a) f_ (1) (x) + lim_ (x rarr a) f (x) + ...... + lim_ (x rarr a) f_ (n) (x)

If 2f(x^2)+3f(1/x^2)=x^2-1 , then f(x^2) is

If f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]

f(x)={(x)/(1+x)+(x)/((1+x)(1+2x))+(x)/((1+2x)(1+3x))+....n terms} and x gt 0 then Lt_(x to oo)f(x)=

If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is continuous at x =1 then

If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is continuous at x =1 then