What is the limit as x approaches 1+of (3+x)/(x^2-1) ?

The limit as x approaches 1+of (3+x)/(x^2-1) is infinity

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limit as x approaches 1+of (3+x)/(x^2-1)

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

\infty

Solution steps

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

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

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

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

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

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

= 4 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

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

8 tan^{2} (8 x)

\frac{d}{d x} (x^{2} - 2 x)

What is the limit as x approaches 1+of (3+x)/(x^2-1) ?
The limit as x approaches 1+of (3+x)/(x^2-1) is infinity