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

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

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

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

\infty

Solution steps

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

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

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

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

Simplify

\frac{x}{x ^{2} ( 1 - \frac{2}{x} - \frac{3}{x ^{2}} )} : \frac{1}{- 2 - \frac{3}{x} + x}

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

For

x

approaching

3

from the right

, x > 3 \Rightarrow - 2 - \frac{3}{x} + x > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

t \to 0 lim (\frac{t ^{2}}{1 - cos ^{2} ( t )})

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

x \to \infty lim (\frac{1}{2} e^{- x^{2}})

x \to 0 lim (\frac{2 x ^{2}}{∣ x ∣})

x \to \infty lim (e^{- 3 s i n (x)})

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