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)

...

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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.**