`f(x)=(ax^2+1)/(x^2+1),lim_(x->0)f(x)=1` and `lim_(x->oo)f(x)=1`,then prove that`f( -2)=f(2)=1`

Let f (x) =(ax+b)/(x+1), lim_(x rarr 0)f(x)=2 and lim_(x to oo)f(x)=1 , Prove that f (- 2) = 0.

It is given that f(x) = (ax+b)/(x+1) , Lim _(x to 0) f(x) and Lim_(x to oo) f(x) = 1 Prove that fx(-2) = 0 .

Given f(x)=(ax+b)/(x+1), lim_(x to oo)f(x)=1 and lim_(x to 0)f(x)=2 , then f(-2) is

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

Sketch the graph of an example of a rational function f that satisfies all the given conditions. (i) f(0)=0,f(1), lim_(xrarroo) f(x)=0,f " is odd" (ii) lim_(xrarr0^(+)) f(x)=oo,lim_(xrarr0^(-)) f(x)=-oo,lim_(xrarroo) f(x)=1,lim_(xrarr-oo) f(x)=1 (iii) lim_(xrarr-2) f(x)=oo, lim_(xrarr-oo) f(x)=3,lim_(xrarroo) f(x) = 3 , f(0)=0

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

if f(x)={-1,AA x 2} then (i)f(x)=1, (ii) lim_(x rarr-1^(+))f(x)=1 (ii) lim_(x rarr2^(+))f(x)=-1(iv)lim_(x rarr2^(-))f(x)=0

if f(2)=4,f'(2)=1 then lim_(x->2){xf(2)-2f(x)}/(x-2)

If alpha in(0,1) and f:R->R and lim_(x->oo)f(x)=0,lim_(x->oo)(f(x)-f(alphax))/x=0, then lim_(x->oo)f(x)/x=lambda where 2lambda+7 is