limit as x approaches 16-of 8/(11+2^{\frac{1){x-16}}}

解

x \to 16 - lim (\frac{8}{11 + 2 ^{\frac{1}{x - 16}}})

\frac{8}{11}

十進法表記

0.72727 \dots

解答ステップ

x \to 16 - lim (\frac{8}{11 + 2 ^{\frac{1}{x - 16}}})

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

= 8 \cdot x \to 16 - lim (\frac{1}{11 + 2 ^{\frac{1}{x - 16}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= 8 \cdot \frac{lim _{x \to 16 -} ( 1 )}{lim _{x \to 16 -} ( 11 + 2 ^{\frac{1}{x - 16}} )}

x \to 16 - lim (1) = 1

x \to 16 - lim (11 + 2^{\frac{1}{x - 16}}) = 11

= 8 \cdot \frac{1}{11}

簡素化

8 \cdot \frac{1}{11} : \frac{8}{11}

= \frac{8}{11}