What is the limit as x approaches-4-of x/((x^2-16)) ?

The limit as x approaches-4-of x/((x^2-16)) is -infinity

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limit as x approaches-4-of x/((x^2-16))

x \to - 4 - lim (\frac{x}{( x ^{2} - 16 )})

- \infty

Solution steps

x \to - 4 - lim (\frac{x}{x ^{2} - 16})

Apply the following algebraic property

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

\frac{x}{x ^{2} - 16} = \frac{x}{x ^{2} ( 1 - \frac{16}{x ^{2}} )}

= x \to - 4 - lim (\frac{x}{x ^{2} ( 1 - \frac{16}{x ^{2}} )})

Cancel the common factor:

x

= x \to - 4 - lim (\frac{1}{x ( - \frac{16}{x ^{2}} + 1 )})

For

x

approaching

- 4

from the left

, x < - 4 \Rightarrow x (- \frac{16}{x ^{2}} + 1) < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

\int \frac{3}{( x + 2 ) ^{2}} d x

\int x (1 - x) d x

t^{2} y^{^{'}} + t y = 6

y = ln (14 x)

\frac{d}{d x} (2 x^{2} - 6 x + 5)

What is the limit as x approaches-4-of x/((x^2-16)) ?
The limit as x approaches-4-of x/((x^2-16)) is -infinity