What is the limit as x approaches 0 of (2^x+x)^{9/x} ?

The limit as x approaches 0 of (2^x+x)^{9/x} is e^{9(ln(2)+1)}

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limit as x approaches 0 of (2^x+x)^{9/x}

x \to 0 lim ((2^{x} + x)^{\frac{9}{x}})

e^{9 (l n (2) + 1)}

Decimal

4148778.97091 \dots

Solution steps

x \to 0 lim ((2^{x} + x)^{\frac{9}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{9}{x} l n (2^{x} + x)})

Apply the Limit Chain Rule:

e^{9 (l n (2) + 1)}

= e^{9 (l n (2) + 1)}

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What is the limit as x approaches 0 of (2^x+x)^{9/x} ?
The limit as x approaches 0 of (2^x+x)^{9/x} is e^{9(ln(2)+1)}