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人気のある微分積分 >

limit as x approaches-4+of x/(x^2-16)

解

x \to - 4 + lim (\frac{x}{x ^{2} - 16})

解

\infty

解答ステップ

x \to - 4 + lim (\frac{x}{x ^{2} - 16})

以下の代数プロパティを適用する

: a + b = a (1 + \frac{b}{a})

\frac{x}{x ^{2} - 16} = \frac{x}{x ^{2} ( 1 - \frac{16}{x ^{2}} )}

= x \to - 4 + lim (\frac{x}{x ^{2} ( 1 - \frac{16}{x ^{2}} )})

共通因数を約分する:

x

= x \to - 4 + lim (\frac{1}{x ( - \frac{16}{x ^{2}} + 1 )})

右側から

- 4

に近づく

x

の場合は,

x > - 4 \Rightarrow x (- \frac{16}{x ^{2}} + 1) > 0

分母は右から0に近づく正の数量

= \infty

グラフ

人気の例

limit as x approaches-1 of 2x^3-5x+6

x \to - 1 lim (2 x^{3} - 5 x + 6)

limit as x approaches 2 of (x-1)/(x^3-3)

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

limit as x approaches 0 of (3x^4+2x^2)/(x^4-x^2)

x \to 0 lim (\frac{3 x ^{4} + 2 x ^{2}}{x ^{4} - x ^{2}})

limit as x approaches 0 of 8xcsc(9x)

x \to 0 lim (8 x csc (9 x))

limit as x approaches 2 of (x-1)/(x^3-1)

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