What is the limit as x approaches 5+of (x+1)/(x-5) ?

The limit as x approaches 5+of (x+1)/(x-5) is infinity

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limit as x approaches 5+of (x+1)/(x-5)

x \to 5 + lim (\frac{x + 1}{x - 5})

\infty

Solution steps

x \to 5 + lim (\frac{x + 1}{x - 5})

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

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

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

x \to 5 + lim (x + 1) = 6

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

= 6 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

f (x) = 8 e^{x} + x, at x = 8

x \to \infty lim (- 1 + e^{(x + 1)})

x \to \infty lim ((6)^{x})

\int \frac{x ^{4} e ^{x} - 4 x ^{3}}{x ^{4}} d x

y^{^{'}} = 9.8 - 0.2 y, y (0) = 100

What is the limit as x approaches 5+of (x+1)/(x-5) ?
The limit as x approaches 5+of (x+1)/(x-5) is infinity