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

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

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

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

e^{3 (l n (2) + 1)}

Decimal

160.68429 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{3 (l n (2) + 1)}

= e^{3 (l n (2) + 1)}

x \to 1 lim (ln (x) + 1)

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

x \to 0 lim (\frac{x}{sin ( - x )})

x \to 1 lim (\frac{7 x - 7}{8 x - 8})

x \to 0 lim (x^{2} \cdot ln ∣ x ∣)

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