Question

Find an even rational function which satisfies all the following conditions:
lim x->∞ f(x)= 4
lim x–>1 f(x)=∞
lim x->0 f(x)=8 although 8 is discontinuous at x=0

Answer 1

lim x->∞ f(x)= 4

\(\dfrac{4x^{2}}{x^{2} - 4}\) -- There are infinitely many. This is just one that I picked.

lim x–>1 f(x)=∞

\(\dfrac{4x^{2}}{x^{2} - 1}\) -- There are infinitely many. This is just one that I picked.

lim x->0 f(x)=8 although 8 is discontinuous at x=0

You figure this one out.