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

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

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

x \to 0 lim (cos^{\frac{1}{x}} (3 x))

1

Solution steps

x \to 0 lim (cos^{\frac{1}{x}} (3 x))

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (c o s (3 x))})

Apply the Limit Chain Rule:

1

= 1

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

x \to 0 + lim (3 x ln (\frac{1}{x}))

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

x \to 0 lim (\frac{4 x}{e ^{x} - 1})

x \to 1 lim (x^{2} - 4 x + 5)

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