What is the limit as x approaches 0 of cos^{3/x}(2x) ?

The limit as x approaches 0 of cos^{3/x}(2x) is 1

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limit as x approaches 0 of cos^{3/x}(2x)

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

1

Solution steps

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

Apply exponent rules

= x \to 0 lim (e^{\frac{3}{x} l n (c o s (2 x))})

Apply the Limit Chain Rule:

1

= 1

x \to - 3 - lim (\frac{3 x}{9 - x ^{2}})

x \to 0 + lim ((x^{2} + 1) ln (x))

x \to 6 lim (3 x - 4)

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

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

What is the limit as x approaches 0 of cos^{3/x}(2x) ?
The limit as x approaches 0 of cos^{3/x}(2x) is 1