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

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

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

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

0

Solution steps

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

Plug in the value

x = 0

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

Simplify

\frac{0 ^{2}}{0 ^{2} - 1} : 0

= 0

x \to 3 - lim (\frac{x + 4}{x + 3})

x \to 2 + lim (\frac{1}{4 - x ^{2}})

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

x \to - 5 lim (\frac{x - 4}{x + 5})

x \to 3 lim (\frac{x + 2}{x ^{2} - 9})

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