What is the limit as x approaches 0 of (5/(1+x)-5)/x ?

The limit as x approaches 0 of (5/(1+x)-5)/x is -5

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limit as x approaches 0 of (5/(1+x)-5)/x

x \to 0 lim (\frac{\frac{5}{1 + x} - 5}{x})

- 5

Solution steps

x \to 0 lim (\frac{\frac{5}{1 + x} - 5}{x})

Simplify

\frac{\frac{5}{1 + x} - 5}{x} : - \frac{5}{1 + x}

= x \to 0 lim (- \frac{5}{1 + x})

Plug in the value

x = 0

= - \frac{5}{1 + 0}

Simplify

= - 5

\frac{d}{d x} (sin (2 x) d x)

(x y sin (x) + 2 y cos (x)) d x + (2 x cos (x)) d y = 0

h \to 0 lim (\frac{( 2 - h ) ^{3} - 8}{h})

\int sin (y^{3}) d y

\frac{\partial}{\partial x} (sin (π (3 x - 5 y)))

What is the limit as x approaches 0 of (5/(1+x)-5)/x ?
The limit as x approaches 0 of (5/(1+x)-5)/x is -5