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

The limit as x approaches 1+of (x^2)/(|1-x|) is infinity

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

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

\infty

Solution steps

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

1 - x

is negative when

x \to 1 +

. Therefore

∣ 1 - x ∣ = - 1 + x

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

\frac{x ^{2}}{- 1 + x} = x^{2} \frac{1}{- 1 + x}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 1 + lim (x^{2}) \cdot x \to 1 + lim (\frac{1}{- 1 + x})

x \to 1 + lim (x^{2}) = 1

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int_{0}^{π} cos (θ) d θ

\frac{d}{d a} (a^{5} + a^{2} b^{3} - a^{3} b^{2} - b^{5})

\int \frac{2}{5} x^{\frac{5}{2}} d x

\frac{d x}{d t} = 4 x - x^{3}

\int_{0}^{\infty} x^{2} e^{- 2 x} d x

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