What is the limit as x approaches-2+of x/(x^2-3x-10) ?

The limit as x approaches-2+of x/(x^2-3x-10) is infinity

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limit as x approaches-2+of x/(x^2-3x-10)

x \to - 2 + lim (\frac{x}{x ^{2} - 3 x - 10})

\infty

Solution steps

x \to - 2 + lim (\frac{x}{x ^{2} - 3 x - 10})

Apply the following algebraic property

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

\frac{x}{x ^{2} - 3 x - 10} = \frac{x}{x ^{2} ( 1 - \frac{3}{x} - \frac{10}{x ^{2}} )}

= x \to - 2 + lim (\frac{x}{x ^{2} ( 1 - \frac{3}{x} - \frac{10}{x ^{2}} )})

Simplify

\frac{x}{x ^{2} ( 1 - \frac{3}{x} - \frac{10}{x ^{2}} )} : \frac{1}{- 3 - \frac{10}{x} + x}

= x \to - 2 + lim (\frac{1}{- 3 - \frac{10}{x} + x})

For

x

approaching

- 2

from the right

, x > - 2 \Rightarrow - 3 - \frac{10}{x} + x > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

y = \frac{x}{10} - \frac{10}{x}

\int \frac{( cos ^{2} ( a t ) )}{a} d x

\frac{d y}{d x}, (7 x y + 5)^{2} = 42 y

\frac{d}{d x} ((7 x^{6} + 4 x^{3})^{4})

\frac{d}{d x} (\frac{x}{( 5 x - 4 ) ^{3}})

What is the limit as x approaches-2+of x/(x^2-3x-10) ?
The limit as x approaches-2+of x/(x^2-3x-10) is infinity