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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

\frac{1}{\frac{9}{x ^{2}} - 1}

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

For

x

approaching

3

from the left

, x < 3 \Rightarrow \frac{9}{x ^{2}} - 1 > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

\int_{0}^{\frac{π}{4}} cos (2 x) d x

y = (3 x^{3} + 7)^{2}

\int (x + 2)^{- 1} d x

\frac{d y}{d x} = 7 x^{2} \cdot \frac{1}{5 y ^{2}}

\frac{d}{d x} (7 x^{\frac{1}{3}})

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