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

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

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

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

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

Decimal Notation

29.55622 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

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

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

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

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

h \to 5 - lim (5 - h)

x \to 0 lim (\frac{2 x - arcsin ( x )}{2 x + arctan ( x )})

x \to 0 + lim (x^{2} ln (4 x^{2}))

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