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Find a reasonable estimate of the limit

Find a reasonable estimate of the limit-example-1
User McLovin
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1 Answer

2 votes

Answer:

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.

User Reader Man San
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