limit as x approaches+1 of (x-1)/(x^6-1)

解答

x \to + 1 lim (\frac{x - 1}{x ^{6} - 1})

\frac{1}{6}

十进制

0.16666 \dots

求解步骤

x \to 1 lim (\frac{x - 1}{x ^{6} - 1})

化简

\frac{x - 1}{x ^{6} - 1} : \frac{1}{( x + 1 ) ( x ^{4} + x ^{2} + 1 )}

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

代入值

x = 1

= \frac{1}{( 1 + 1 ) ( 1 ^{4} + 1 ^{2} + 1 )}

化简

= \frac{1}{6}

x \to 0 lim (\frac{3 x}{sin ( 10 x )})

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