limit as x approaches 1 of (x^{22}-2x+1)/(x^3-2x+1)

解答

x \to 1 lim (\frac{x ^{22} - 2 x + 1}{x ^{3} - 2 x + 1})

20

求解步骤

x \to 1 lim (\frac{x ^{22} - 2 x + 1}{x ^{3} - 2 x + 1})

化简

\frac{x ^{22} - 2 x + 1}{x ^{3} - 2 x + 1} : \frac{x ^{21} + x ^{20} + x ^{19} + x ^{18} + x ^{17} + x ^{16} + x ^{15} + x ^{14} + x ^{13} + x ^{12} + x ^{11} + x ^{10} + x ^{9} + x ^{8} + x ^{7} + x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x - 1}{x ^{2} + x - 1}

= x \to 1 lim (\frac{x ^{21} + x ^{20} + x ^{19} + x ^{18} + x ^{17} + x ^{16} + x ^{15} + x ^{14} + x ^{13} + x ^{12} + x ^{11} + x ^{10} + x ^{9} + x ^{8} + x ^{7} + x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x - 1}{x ^{2} + x - 1})

代入值

x = 1

= \frac{1 ^{21} + 1 ^{20} + 1 ^{19} + 1 ^{18} + 1 ^{17} + 1 ^{16} + 1 ^{15} + 1 ^{14} + 1 ^{13} + 1 ^{12} + 1 ^{11} + 1 ^{10} + 1 ^{9} + 1 ^{8} + 1 ^{7} + 1 ^{6} + 1 ^{5} + 1 ^{4} + 1 ^{3} + 1 ^{2} + 1 - 1}{1 ^{2} + 1 - 1}

化简

= 20

x \to \infty lim ((+ x)^{2})

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n \to \infty lim (\frac{n n - 1}{n ^{2} + 1})

x \to 0 lim (x csc (x) sec (x))