What is the limit as x approaches 0+of (x+cos(x))^{4/x} ?

The limit as x approaches 0+of (x+cos(x))^{4/x} is e^4

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limit as x approaches 0+of (x+cos(x))^{4/x}

x \to 0 + lim ((x + cos (x))^{\frac{4}{x}})

e^{4}

Decimal

54.59815 \dots

Solution steps

x \to 0 + lim ((x + cos (x))^{\frac{4}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{4}{x} l n (x + c o s (x))})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

What is the limit as x approaches 0+of (x+cos(x))^{4/x} ?
The limit as x approaches 0+of (x+cos(x))^{4/x} is e^4