What is the limit as x approaches 0 of 2xcos(1/x)-2 ?

The limit as x approaches 0 of 2xcos(1/x)-2 is -2

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limit as x approaches 0 of 2xcos(1/x)-2

x \to 0 lim (2 x cos (\frac{1}{x}) - 2)

- 2

Solution steps

x \to 0 lim (2 x cos (\frac{1}{x}) - 2)

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 (2 x cos (\frac{1}{x})) - x \to 0 lim (2)

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

x \to 0 lim (2) = 2

= 0 - 2

Simplify

= - 2

f (x) = (4 x + 2)^{- 1}

\int (\frac{1}{9 + x ^{2}}) d x

\int \frac{1}{sec ( y ) tan ( y )} d y

y^{^{'}} + 2 y = e^{3 x}

\frac{d}{d x} (5 tan (2 x^{3}))

What is the limit as x approaches 0 of 2xcos(1/x)-2 ?
The limit as x approaches 0 of 2xcos(1/x)-2 is -2