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

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

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

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

2

Solution steps

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

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

x \to 0 lim (2) = 2

= 0 + 2

Simplify

= 2

n \to \infty lim (sin (2 πn))

x \to 0 lim (x^{3} - x^{2})

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

x \to 1 lim (x^{2} + 3 x - 5)

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

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