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 diverges

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

= diverges

x^{^{''}} + \frac{9}{4} x^{^{'}} + \frac{9}{64} x = 0, x^{^{'}} (0) = 1, x (0) = 2

n = 0 \sum \infty \frac{1}{n ^{0.51}}

\frac{d v}{d t} = 10 - 2 v

y^{^{''}} - 2 y = 9 x e^{- x}

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 diverges