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

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

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

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

\infty

Solution steps

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

Simplify

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

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

Divide by highest denominator power:

\frac{1}{1 - \frac{1}{x}}

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

For

x

approaching

1

from the right

, x > 1 \Rightarrow 1 - \frac{1}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

\frac{d}{d a} (sin (a) + cos (a))

\frac{4}{ln ( x )}

x \to \frac{23}{2} lim (\frac{3}{2})

\int x^{2} ln (7 x) d x

\int \frac{4}{5} - \frac{7}{x} d x

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