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)
...
See This Answer Now
Start your subscription to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.
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.