What is the limit as x approaches 0 of (5/(6+x)-5/6)/x ?

The limit as x approaches 0 of (5/(6+x)-5/6)/x is -5/36

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limit as x approaches 0 of (5/(6+x)-5/6)/x

x \to 0 lim (\frac{\frac{5}{6 + x} - \frac{5}{6}}{x})

- \frac{5}{36}

Decimal Notation

- 0.13888 \dots

Solution steps

x \to 0 lim (\frac{\frac{5}{6 + x} - \frac{5}{6}}{x})

Simplify

\frac{\frac{5}{6 + x} - \frac{5}{6}}{x} : - \frac{5}{6 ( x + 6 )}

= x \to 0 lim (- \frac{5}{6 ( x + 6 )})

Plug in the value

x = 0

= - \frac{5}{6 ( 0 + 6 )}

Simplify

= - \frac{5}{36}

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x \to 0 lim (\frac{- 1}{0})

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x \to \infty lim (8 + 2 (- 4))

x \to 0 lim (\frac{e ^{s i n (x)} - e ^{t a n (x)}}{sin ( x ) - tan ( x )})

What is the limit as x approaches 0 of (5/(6+x)-5/6)/x ?
The limit as x approaches 0 of (5/(6+x)-5/6)/x is -5/36