A student applies L'Hôpital to lim _x→0(x+1)/(x+2) and gets 1. What went wrong?

The error is that (x+1)/(x+2) is not indeterminate at 0; the correct limit is 1/2

The error is that it should be differentiated three times

There is no error: the limit is 1

The error is that the limit is 0

Exercise · ZW-LHOPITALS-RULE-019 · ★★☆ Intermediate

A student applies L'Hôpital to \(\lim_{x\to0}\frac{x+1}{x+2}\) and gets \(1\). What went wrong?

Choose one option.

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A. The error is that (x+1)/(x+2) is not indeterminate at 0; the correct limit is 1/2

Explanation

The quotient tends to \(\frac12\), which is not an indeterminate form. The rule requires \(0/0\) or \(\infty/\infty\); otherwise it gives false results.

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Review the concept: L'Hôpital's rule

Rule that computes limits of quotients in indeterminate form \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\) by differentiating numerator and denominator separately.

\[\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}\]

A student applies L'Hôpital to \(\lim_{x\to0}\frac{x+1}{x+2}\) and gets \(1\). What went wrong?

Explanation

Review the concept: L'Hôpital's rule

More practice problems: l'hôpital's rule