What is the limit as h approaches 0 of (ln(3+h)-ln(3))/h ?

The limit as h approaches 0 of (ln(3+h)-ln(3))/h is 1/3

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limit as h approaches 0 of (ln(3+h)-ln(3))/h

h \to 0 lim (\frac{ln ( 3 + h ) - ln ( 3 )}{h})

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

h \to 0 lim (\frac{ln ( 3 + h ) - ln ( 3 )}{h})

Apply L'Hopital's Rule

: h \to 0 lim (\frac{\frac{1}{h + 3}}{1})

= h \to 0 lim (\frac{\frac{1}{h + 3}}{1})

Plug in the value

h = 0

= \frac{\frac{1}{0 + 3}}{1}

Simplify

= \frac{1}{3}

x \to 0 + lim (\frac{ln ( 1 + x )}{x})

x \to 0 + lim (1^{\frac{l n ( 6 )}{x}})

x \to 0 lim ((1 + 8 x)^{\frac{1}{x}})

x \to - 1 - lim (- \frac{1}{x + 1})

x \to - 3 lim (\frac{4 - x ^{2}}{x + 3})

What is the limit as h approaches 0 of (ln(3+h)-ln(3))/h ?
The limit as h approaches 0 of (ln(3+h)-ln(3))/h is 1/3