Let . Prove that by exhibiting an explicit in terms of that fulfils the ε–M…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\dfrac{4x^{2}-1}{2x^{2}+5}

. Prove that

\displaystyle\lim_{x\to\infty}f(x)=2

by exhibiting an explicit

M

in terms of

\varepsilon>0

that fulfils the ε–M criterion.