Question

Find a reasonable estimate of the limit

Answer 1

A) 1.25

Explanation:

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

`\lim_(x \to 3) (x^(2)-x-6 )/(x^(2)-2x-3)`

`\lim_(x \to 3) (2x-1-0 )/(2x-2-0)`

`\lim_(x \to 3) (2x-1)/(2x-2)`

Substitute x=3 into the expression:

`(2(3)-1)/(2(3)-2)`

`(6-1)/(6-2)`

`(5)/(4)`

Therefore,
`\lim_(x \to 3) (x^(2)-x-6 )/(x^(2)-2x-3)=(5)/(4)=1.25`, making the correct answer A.