What is the limit as x approaches 0+of (2+sin(x))/x ?

The limit as x approaches 0+of (2+sin(x))/x is infinity

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limit as x approaches 0+of (2+sin(x))/x

x \to 0 + lim (\frac{2 + sin ( x )}{x})

\infty

Solution steps

x \to 0 + lim (\frac{2 + sin ( x )}{x})

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

= x \to 0 + lim ((2 + sin (x)) \frac{1}{x})

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 0 + lim (2 + sin (x)) \cdot x \to 0 + lim (\frac{1}{x})

x \to 0 + lim (2 + sin (x)) = 2

x \to 0 + lim (\frac{1}{x}) = \infty

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 - lim (\frac{- 2}{x ^{4}})

x \to 5 lim (\frac{∣ x - 5 ∣}{x + 1})

x \to - 5 + lim (\frac{- 3 x}{x + 5})

x \to 3 - lim (arcsin (\frac{x}{3}))

t \to 3 lim (\frac{t ^{2} - 9}{t - 3})

What is the limit as x approaches 0+of (2+sin(x))/x ?
The limit as x approaches 0+of (2+sin(x))/x is infinity