What is the limit as x approaches 0+of x(1-cos(1/x)) ?

The limit as x approaches 0+of x(1-cos(1/x)) is 0

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limit as x approaches 0+of x(1-cos(1/x))

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

0

Solution steps

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

Expand

x (1 - cos (\frac{1}{x})) : x - x cos (\frac{1}{x})

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to 0 + lim (x) = 0

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

= 0 - 0

Simplify

= 0

\int \frac{1}{x ^{2} \cdot x ^{2} + 4} d x

\frac{d x}{d t} - 5 x = sin (2 t), x (0) = π

\int tan^{5} (3 x) d x

\int \frac{4}{x ^{2} - 2 x} d x

5 sin (2 t)

What is the limit as x approaches 0+of x(1-cos(1/x)) ?
The limit as x approaches 0+of x(1-cos(1/x)) is 0