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

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

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limit as x approaches 0+of (cos(x))/x

x \to 0 + lim (\frac{cos ( x )}{x})

\infty

Solution steps

x \to 0 + lim (\frac{cos ( x )}{x})

\frac{cos ( x )}{x} = cos (x) \frac{1}{x}

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

x \to 0 + lim (cos (x)) = 1

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

n \to \infty lim (n! + n^{3})

y^{^{''}} = 4 y, y^{^{'}} (0) = 1, y (0) = 0

y^{^{''}} - 18 y^{^{'}} + 81 y = t^{- 2} e^{9 t}

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

\frac{d}{d x} (\frac{5 ^{x}}{cos ( x )})

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