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

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

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

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

\infty

Solution steps

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

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

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

x \to 2 + lim (2 x + 1) = 5

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

= 5 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

cos (x^{5})

n = 0 \sum \infty (\frac{π}{e})^{n}

\frac{e ^{- 2 x}}{2 x ^{2} + 1}

y^{^{''}} - 3 y^{^{'}} - 10 y = 4 e^{4 t}, y (0) = 0, y^{^{'}} (0) = 0

x \to - 3 lim (2 x^{2} + 4 x + 1)

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