What is the limit as x approaches 2-of (x+1)/(4-x^2) ?

The limit as x approaches 2-of (x+1)/(4-x^2) is infinity

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limit as x approaches 2-of (x+1)/(4-x^2)

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

\infty

Solution steps

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

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

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

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

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

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int 3 - t^{2} d t

f (t) = \frac{2 t + 1}{t + 3}

\int \frac{x ^{2}}{1 - x ^{3}} d x

\int \frac{2}{x ^{2} + 16} d x

\int_{2}^{\infty} \frac{5}{x ^{2}} d x

What is the limit as x approaches 2-of (x+1)/(4-x^2) ?
The limit as x approaches 2-of (x+1)/(4-x^2) is infinity