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

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

Popular >

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

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

- \infty

Solution steps

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

Multiply by the conjugate of

3 + x : \frac{9 - x ^{2}}{3 - x}

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

Simplify

\frac{\frac{9 - x ^{2}}{3 - x}}{9 - x ^{2}} : \frac{1}{3 - x}

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

For

x

approaching

3

from the right

, x > 3 \Rightarrow 3 - x < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

z \to i lim (z^{2})

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

x \to - 2 lim (6 x^{3} - 2 x^{2} + 7)

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

x \to 3 + lim (3 - x)

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