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

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

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limit as x approaches 0 of xcos(2x)

x \to 0 lim (x cos (2 x))

0

Solution steps

x \to 0 lim (x cos (2 x))

Plug in the value

x = 0

= 0 \cdot cos (2 \cdot 0)

Simplify

0 \cdot cos (2 \cdot 0) : 0

= 0

x \to 0 lim (sin (x) cos (x))

x \to \infty lim (- 8 (\frac{3}{x}))

x \to \infty lim (\frac{\frac{1}{x}}{\frac{1}{2 x}})

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x \to 0 lim (\frac{5 ^{x} - 6 ^{x}}{x})

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