What is the limit as x approaches 5 of ((ln(x/5)))/(x^2-25) ?

The limit as x approaches 5 of ((ln(x/5)))/(x^2-25) is 1/50

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limit as x approaches 5 of ((ln(x/5)))/(x^2-25)

x \to 5 lim (\frac{( ln ( \frac{x}{5} ) )}{x ^{2} - 25})

\frac{1}{50}

Decimal Notation

0.02

Solution steps

x \to 5 lim (\frac{ln ( \frac{x}{5} )}{x ^{2} - 25})

Apply L'Hopital's Rule

: x \to 5 lim (\frac{\frac{1}{x}}{2 x})

= x \to 5 lim (\frac{\frac{1}{x}}{2 x})

Plug in the value

x = 5

= \frac{\frac{1}{5}}{2 \cdot 5}

Simplify

\frac{\frac{1}{5}}{2 \cdot 5} : \frac{1}{50}

= \frac{1}{50}

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What is the limit as x approaches 5 of ((ln(x/5)))/(x^2-25) ?
The limit as x approaches 5 of ((ln(x/5)))/(x^2-25) is 1/50