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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

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

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

For

t

approaching

3

from the left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

\int \frac{x ^{2}}{x ^{2} + 8} d x

\frac{e ^{x} - 1}{x ^{2} + 1}

y^{^{''}} - 4 y^{^{'}} + 4 = 0

n = 0 \sum \infty \frac{( 3 ^{n} )}{n !}

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

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