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人気のある微分積分 >

limit as x approaches 5-of (sin((x-7)(x-5)))/(x-5)

解

x \to 5 - lim (\frac{sin ( ( x - 7 ) ( x - 5 ) )}{x - 5})

解

- 2

解答ステップ

x \to 5 - lim (\frac{sin ( ( x - 7 ) ( x - 5 ) )}{x - 5})

x

を

x - 7 : x (1 - \frac{7}{x})

からくくり出す

= x \to 5 - lim (\frac{sin ( x ( 1 - \frac{7}{x} ) ( x - 5 ) )}{x - 5})

拡張

x (1 - \frac{7}{x}) (x - 5) : x^{2} + 35 - 12 x

= x \to 5 - lim (\frac{sin ( x ^{2} + 35 - 12 x )}{x - 5})

ロピタルの定理を適用する

= x \to 5 - lim (\frac{cos ( x ^{2} + 35 - 12 x ) ( 2 x - 12 )}{1})

値を挿入する

x = 5

= \frac{cos ( 5 ^{2} + 35 - 12 \cdot 5 ) ( 2 \cdot 5 - 12 )}{1}

簡素化

\frac{cos ( 5 ^{2} + 35 - 12 \cdot 5 ) ( 2 \cdot 5 - 12 )}{1} : - 2

= - 2

グラフ

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