Question

Find a reasonable estimate of the limit

Answer 1

Answer:

A) 1.25

Step-by-step explanation:

Use L'Hôpital's Rule and differentiate both top and bottom expressions:

$\lim_{x \to 3} \frac{x^{2}-x-6 }{x^{2}-2x-3}$

$\lim_{x \to 3} \frac{2x-1-0 }{2x-2-0}$

$\lim_{x \to 3} \frac{2x-1}{2x-2}$

Substitute x=3 into the expression:

$\frac{2(3)-1}{2(3)-2}$

$\frac{6-1}{6-2}$

$\frac{5}{4}$

Therefore, $\lim_{x \to 3} \frac{x^{2}-x-6 }{x^{2}-2x-3}=\frac{5}{4}=1.25$, making the correct answer A.