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

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

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limit as x approaches 0 of x*cos(1/x)

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

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

3 x^{2} - 5 x + 2

x \to - 9 - lim (\frac{1}{( x + 9 ) ^{2}})

\frac{d}{d x} ((9 x + 3) e^{2 x^{2} + 3})

(y - \frac{y}{x ^{2}} e^{\frac{y}{x}}) d x + (x + \frac{1}{x} e^{\frac{y}{x}}) d y = 0

\frac{d}{d x} (\frac{x ^{2} + 5 x - 1}{x ^{2}})

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