What is the limit as x approaches 1-of 3/(x^2-1) ?

The limit as x approaches 1-of 3/(x^2-1) is -infinity

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limit as x approaches 1-of 3/(x^2-1)

x \to 1 - lim (\frac{3}{x ^{2} - 1})

- \infty

Solution steps

x \to 1 - lim (\frac{3}{x ^{2} - 1})

For

x

approaching

1

from the left

, x < 1 \Rightarrow x^{2} - 1 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

y = - x^{2} + 5 x - 3, y = x^{2} - 3 x + 3

\frac{\partial}{\partial y} (e^{y - x})

\frac{d y}{d x} = - e^{x + y}

y = 9 - x^{2}, y = 0

y = (5 - x^{2}) (x^{3} - 3 x + 2)

What is the limit as x approaches 1-of 3/(x^2-1) ?
The limit as x approaches 1-of 3/(x^2-1) is -infinity