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

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

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

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

\infty

Solution steps

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

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

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

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

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

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

y^{^{''}} + 12 y^{^{'}} + 37 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int_{0}^{1} \frac{23}{4 y - 1} d y

f (x) = cos^{3} (π x)

\int \frac{x ^{2} - 400}{x} d x

\int \frac{0}{x + 1} d x

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