What is the limit as x approaches 0 of ((ln(2e+x)-ln(2e)))/x ?

The limit as x approaches 0 of ((ln(2e+x)-ln(2e)))/x is 1/(2e)

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limit as x approaches 0 of ((ln(2e+x)-ln(2e)))/x

x \to 0 lim (\frac{( ln ( 2 e + x ) - ln ( 2 e ) )}{x})

\frac{1}{2 e}

Decimal

0.18393 \dots

Solution steps

x \to 0 lim (\frac{ln ( 2 e + x ) - ln ( 2 e )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{\frac{1}{x + 2 e}}{1})

= x \to 0 lim (\frac{\frac{1}{x + 2 e}}{1})

Plug in the value

x = 0

= \frac{\frac{1}{0 + 2 e}}{1}

Simplify

= \frac{1}{2 e}

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What is the limit as x approaches 0 of ((ln(2e+x)-ln(2e)))/x ?
The limit as x approaches 0 of ((ln(2e+x)-ln(2e)))/x is 1/(2e)