What is the limit as x approaches 2+of (x^2)/(x^2-4) ?

The limit as x approaches 2+of (x^2)/(x^2-4) is infinity

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limit as x approaches 2+of (x^2)/(x^2-4)

x \to 2 + lim (\frac{x ^{2}}{x ^{2} - 4})

\infty

Solution steps

x \to 2 + lim (\frac{x ^{2}}{x ^{2} - 4})

Divide by highest denominator power:

\frac{1}{1 - \frac{4}{x ^{2}}}

= x \to 2 + lim (\frac{1}{1 - \frac{4}{x ^{2}}})

For

x

approaching

2

from the right

, x > 2 \Rightarrow 1 - \frac{4}{x ^{2}} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

1 - (1 - 0.01 x)^{3}

\int_{0}^{1} 11 x x^{2} + 16 d x

x = \frac{1}{2} y^{2} - 3, x = y + 1

f (x) = x + 6

n = 1 \sum \infty n^{\frac{3}{4}}

What is the limit as x approaches 2+of (x^2)/(x^2-4) ?
The limit as x approaches 2+of (x^2)/(x^2-4) is infinity