What is the limit as x approaches 0 of ((1/((x+4)))-(1/4))/x ?

The limit as x approaches 0 of ((1/((x+4)))-(1/4))/x is -1/16

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limit as x approaches 0 of ((1/((x+4)))-(1/4))/x

x \to 0 lim \frac{( \frac{1}{( x + 4 )} ) - ( \frac{1}{4} )}{x}

- \frac{1}{16}

Decimal

- 0.0625

Solution steps

x \to 0 lim (\frac{\frac{1}{x + 4} - \frac{1}{4}}{x})

Simplify

\frac{\frac{1}{x + 4} - \frac{1}{4}}{x} : - \frac{1}{4 ( x + 4 )}

= x \to 0 lim (- \frac{1}{4 ( x + 4 )})

Plug in the value

x = 0

= - \frac{1}{4 ( 0 + 4 )}

Simplify

= - \frac{1}{16}

d er i v a t i v e 5 x + 8

y^{^{'}} = \frac{x}{1 + x ^{2}}

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{x})

y^{^{'}} = y^{2} - (x y)^{2}

\int \frac{1}{3 x ( 2 + x )} d x

What is the limit as x approaches 0 of ((1/((x+4)))-(1/4))/x ?
The limit as x approaches 0 of ((1/((x+4)))-(1/4))/x is -1/16