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

解

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

14

解答ステップ

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 )}})

指数の規則を適用する

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

連鎖法則の制限を適用する:

2

= 7 \cdot 2

簡素化

= 14