Question

Confirm that the below limit meets the conditions to apply l'Hôpital's Rule and then solve the limit. Be sure to address these conditions in your explanation. Enter an exact numeric answer. limx→0+6sin(x)7ln(1+x)limx→0+6sin⁡(x)7ln⁡(1+x)

Name: confirm that the below limit meets the conditions to apply lhopitals rule and then solve the limit be sure to address these conditions in your explanation enter an exact numeric answer limx0 69223
Uploaded: 2023-08-04T00:50:57-08:00
Duration: 1 min 13 s
Channel: Bradley Duda
Description: confirm that the below limit meets the conditions to apply lhopitals rule and then solve the limit be sure to address these conditions in your explanation enter an exact numeric answer limx0 69223

          Confirm that the below limit meets the conditions to apply l'Hôpital's Rule and then solve the limit. Be sure to address these conditions in your explanation.
Enter an exact numeric answer.
limx→0+6sin(x)7ln(1+x)limx→0+6sin⁡(x)7ln⁡(1+x)

Added by Claudia R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Bradley Duda

08/04/2023

Step 1

Given limit: \[ \lim_{x \to 0^+} \frac{6 \sin(x)}{7 \ln(1+x)} \] As \(x \to 0^+\), evaluate numerator and denominator separately: - \(\sin(0) = 0\) - \(\ln(1+0) = \ln(1) = 0\) So the limit is of the form \(\frac{0}{0}\), which is an indeterminate form. Show more…

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Confirm that the below limit meets the conditions to apply l'Hôpital's Rule and then solve the limit. Be sure to address these conditions in your explanation. Enter an exact numeric answer. limx→0+6sin(x)7ln(1+x)limx→0+6sin⁡(x)7ln⁡(1+x)