What is the limit as x approaches 3+of (4-x)/(9-x^2) ?

The limit as x approaches 3+of (4-x)/(9-x^2) is -infinity

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limit as x approaches 3+of (4-x)/(9-x^2)

x \to 3 + lim (\frac{4 - x}{9 - x ^{2}})

- \infty

Solution steps

x \to 3 + lim (\frac{4 - x}{9 - x ^{2}})

\frac{4 - x}{9 - x ^{2}} = (4 - x) \frac{1}{9 - x ^{2}}

= x \to 3 + lim ((4 - x) \frac{1}{9 - x ^{2}})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 3 + lim (4 - x) \cdot x \to 3 + lim (\frac{1}{9 - x ^{2}})

x \to 3 + lim (4 - x) = 1

x \to 3 + lim (\frac{1}{9 - x ^{2}}) = - \infty

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\int \frac{sin ( 3 x )}{3 + 3 cos ( 3 x )} d x

\frac{d y}{d x}, 3 x y = 6

\int_{- 1}^{2} (x^{3}) d x

f (x) = 2 x + 1, 1, 5

What is the limit as x approaches 3+of (4-x)/(9-x^2) ?
The limit as x approaches 3+of (4-x)/(9-x^2) is -infinity