What is the limit as x approaches infinity of 7x^{(ln(2))/(7+ln(x))} ?

The limit as x approaches infinity of 7x^{(ln(2))/(7+ln(x))} is 14

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limit as x approaches infinity of 7x^{(ln(2))/(7+ln(x))}

x \to \infty lim (7 x^{\frac{l n ( 2 )}{7 + l n ( x )}})

14

Solution steps

x \to \infty lim (7 x^{\frac{l n ( 2 )}{7 + l n ( x )}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to \infty lim (x^{\frac{l n ( 2 )}{7 + l n ( x )}})

Apply exponent rules

= 7 \cdot x \to \infty lim (e^{\frac{l n ( 2 )}{7 + l n ( x )} l n (x)})

Apply the Limit Chain Rule:

2

= 7 \cdot 2

Simplify

= 14

x \to 0 - lim (\frac{sin ( 3 x )}{x})

x \to 7 lim (\frac{8}{x ^{2} - 49})

x \to \infty lim (2 x + \frac{5}{x})

x \to 3 lim (\frac{1}{x ^{2}})

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

What is the limit as x approaches infinity of 7x^{(ln(2))/(7+ln(x))} ?
The limit as x approaches infinity of 7x^{(ln(2))/(7+ln(x))} is 14