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

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

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limit as x approaches 0 of x/(1-(x-1)^2)

x \to 0 lim (\frac{x}{1 - ( x - 1 ) ^{2}})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (\frac{x}{1 - ( x - 1 ) ^{2}})

Simplify

\frac{x}{1 - ( x - 1 ) ^{2}} : - \frac{1}{x - 2}

= x \to 0 lim (- \frac{1}{x - 2})

Plug in the value

x = 0

= - \frac{1}{0 - 2}

Simplify

= \frac{1}{2}

t \to 0 + lim (arctan (ln (t)))

\frac{9}{x}, 1

\int \frac{2 x}{x ^{4} + 25} d x

ln (1 + \frac{3}{x} + \frac{5}{x ^{2}})

\int (x^{4} + 3)^{\frac{3}{2}} x^{3} d x

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