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

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

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limit as x approaches infinity of (x)^{(ln(2))/(1+ln(x))}

x \to \infty lim ((x)^{\frac{l n ( 2 )}{1 + l n ( x )}})

2

Solution steps

x \to \infty lim (x^{\frac{l n ( 2 )}{1 + l n ( x )}})

Apply exponent rules

= x \to \infty lim (e^{\frac{l n ( 2 )}{1 + l n ( x )} l n (x)})

Apply the Limit Chain Rule:

2

= 2

f (x) = \frac{100}{( 1 + 5 x ) ^{3}}

\int x^{3} + sin (x) + cos (x) d x

\int e^{8 x} sin (9 x) d x

f (x) = tan^{2} (3 e^{x})

\frac{7}{( 2 x + 1 ) ^{2}}

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