Answer
a) 2; b) 0;
Work Step by Step
We are given the function:
$g(x)=\dfrac{e^{2x}-2x-1}{x^2}$
a) Graph $g$ to estimate $\lim\limits_{x \to 0} g(x)$:
From the graph we find:
$\lim\limits_{x \to 0} g(x)=2$
b) Evaluate $g(x)$ for values near 0:
$g(-0.1)\approx 1.87331$
$g(-0.01)\approx 1.98673$
$g(-0.001)\approx 1.99867$
$g(0.001)\approx 2.001334$
$g(0.01)\approx 2.013400$
$g(0.1)\approx 2.140276$
The values we found prove that the conjecture from part $a)$ is true:
$\lim\limits_{x \to 0} g(x)=2$
