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

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

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

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

\frac{3}{e}

Decimal Notation

1.10363 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

h = 0

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

Simplify

= \frac{3}{e}

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(- 9, - 6), (3, - 9)

x e^{2 y} \frac{d y}{d x} + e^{2 y} = \frac{ln ( x )}{x}

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