What is the limit as x approaches 5+of (sqrt(x^2-25))/(x-5) ?

The limit as x approaches 5+of (sqrt(x^2-25))/(x-5) is infinity

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limit as x approaches 5+of (sqrt(x^2-25))/(x-5)

x \to 5 + lim (\frac{x ^{2} - 25}{x - 5})

\infty

Solution steps

x \to 5 + lim (\frac{x ^{2} - 25}{x - 5})

Rationalize numerator

\frac{x ^{2} - 25}{x - 5} : \frac{x + 5}{x ^{2} - 25}

= x \to 5 + lim (\frac{x + 5}{x ^{2} - 25})

\frac{x + 5}{x ^{2} - 25} = (x + 5) \frac{1}{x ^{2} - 25}

= x \to 5 + lim ((x + 5) \frac{1}{x ^{2} - 25})

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 5 + lim (x + 5) \cdot x \to 5 + lim (\frac{1}{x ^{2} - 25})

x \to 5 + lim (x + 5) = 10

x \to 5 + lim (\frac{1}{x ^{2} - 25}) = \infty

= 10 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\frac{\partial}{\partial x} (5 x^{9 y})

\int - \frac{4}{s + 1} d s

\int (2 x^{2} - x - 7) d x

\frac{\partial}{\partial x} (ln (3 x + 6 y + 9 z))

\frac{d y}{d x} = x e^{x + y}

What is the limit as x approaches 5+of (sqrt(x^2-25))/(x-5) ?
The limit as x approaches 5+of (sqrt(x^2-25))/(x-5) is infinity