What is the limit as x approaches 0 of (4/(2+x)-2)/x ?

The limit as x approaches 0 of (4/(2+x)-2)/x is -1

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limit as x approaches 0 of (4/(2+x)-2)/x

x \to 0 lim (\frac{\frac{4}{2 + x} - 2}{x})

- 1

Solution steps

x \to 0 lim (\frac{\frac{4}{2 + x} - 2}{x})

Simplify

\frac{\frac{4}{2 + x} - 2}{x} : - \frac{2}{2 + x}

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

Plug in the value

x = 0

= - \frac{2}{2 + 0}

Simplify

= - 1

\int 5 sin (3 x) d x

y = lo g_{3} (5 x^{4})

2 x^{2} + y^{2} - 7 = 0

\int_{π}^{2 π} - cos (x) d x

x \to 1 lim (\frac{x - x ^{3}}{x - 1})

What is the limit as x approaches 0 of (4/(2+x)-2)/x ?
The limit as x approaches 0 of (4/(2+x)-2)/x is -1