What is the limit as x approaches 0 of x^8cos(1/x) ?

The limit as x approaches 0 of x^8cos(1/x) is 0

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limit as x approaches 0 of x^8cos(1/x)

x \to 0 lim (x^{8} cos (\frac{1}{x}))

0

Solution steps

x \to 0 lim (x^{8} cos (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= 0

x \to 0 lim (tan (x) - x)

y \to 3 lim (\frac{y ^{3} - 13 y + 12}{y ^{3} - 14 y + 15})

x \to 0 lim (\frac{tan ( 4 x )}{2 x})

x \to - 7 lim (\frac{4 x - 1}{x + 7})

x \to 8 + lim (\frac{x}{x - 8})

What is the limit as x approaches 0 of x^8cos(1/x) ?
The limit as x approaches 0 of x^8cos(1/x) is 0