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 7 - lim (\frac{[ x ] - x}{x - 7})

x \to 0 lim (5 x cot (x))

x \to 3 lim (\frac{x - 1}{6 - 2 x})

x \to 2 lim (3 x^{2} - 4 x)

x \to 8 lim (2 x \cdot 2 x)

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