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

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

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

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

1

Solution steps

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

Simplify

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

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

Plug in the value

x = 0

= \frac{1}{0 + 1}

Simplify

= 1

(0, 0), (5, 4)

x \to 2 π lim (x csc (x))

\frac{e ^{x}}{1 - e ^{x}}

\int - 2 x e^{- x} d x

\int_{1}^{2} (y^{3} + \frac{1}{4 y ^{3}}) d y

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