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

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

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

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

- \infty

Solution steps

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

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

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

For

x

approaching

3

from the right

, x > 3 \Rightarrow x^{2} - 9 > 0

The denominator is a positive quantity approaching 0 from the right

= - 2 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int 5 e^{- 0.4 x} d x

t an g e n t f (x) = 7 sec (x), at x = \frac{π}{6}

x \to a lim (\frac{1}{0})

\int_{0}^{7} x^{2} + 49 d x

\int (\frac{2}{x} + \frac{x}{2}) d x

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