What is the limit as x approaches-3+of x/(x^2-9) ?

The limit as x approaches-3+of x/(x^2-9) is infinity

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limit as x approaches-3+of x/(x^2-9)

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

\infty

Solution steps

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

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

\frac{x}{x ^{2} - 9} = \frac{x}{x ^{2} ( 1 - \frac{9}{x ^{2}} )}

= x \to - 3 + lim (\frac{x}{x ^{2} ( 1 - \frac{9}{x ^{2}} )})

Cancel the common factor:

x

= x \to - 3 + lim (\frac{1}{x ( - \frac{9}{x ^{2}} + 1 )})

For

x

approaching

- 3

from the right

, x > - 3 \Rightarrow x (- \frac{9}{x ^{2}} + 1) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

x \to 2 lim (\frac{x ^{3} - 8}{2 x})

\frac{\partial}{\partial x} (x e^{x y} - 2 y + 1)

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

\frac{d}{d x} (e^{x^{2} + y^{2}})

\frac{d}{d x} (0.005 x^{2} - ln (x^{16}) + 70)

What is the limit as x approaches-3+of x/(x^2-9) ?
The limit as x approaches-3+of x/(x^2-9) is infinity