Verify if limit of ln(1+x)/x is 1, x-->0

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to verify that lim x-->0 [ ln(1+x)/x] = 1.

substituting x = 0, we get the indeterminate form 0/0, therefore we can use the l'Hopital's rule and substitute the numerator and denominator with their derivatives.

=> lim x-->0 [ ((1/(1+x))/1]

substituting x = 0

=> 1/(1 + 0)

=> 1

This verifies that lim x-->0 [ ln(1+x)/x] = 1.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team