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求(3n-sin(n^2))/(2n+cos(n^2))的极限,当n趋于无限大时
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求(3n-sin(n^2))/(2n+cos(n^2))的极限,当n趋于无限大时
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答案和解析
(3n-1)/(2n+1) ≤(3n-sin(n^2))/(2n+cos(n^2))≤ (3n +1)/(2n-1)
lim(n->∞)(3n-1)/(2n+1) ≤lim(n->∞)(3n-sin(n^2))/(2n+cos(n^2))≤ lim(n->∞)(3n +1)/(2n-1)
3/2≤lim(n->∞)(3n-sin(n^2))/(2n+cos(n^2))≤3/2
=> lim(n->∞)(3n-sin(n^2))/(2n+cos(n^2)) =3/2
lim(n->∞)(3n-1)/(2n+1) ≤lim(n->∞)(3n-sin(n^2))/(2n+cos(n^2))≤ lim(n->∞)(3n +1)/(2n-1)
3/2≤lim(n->∞)(3n-sin(n^2))/(2n+cos(n^2))≤3/2
=> lim(n->∞)(3n-sin(n^2))/(2n+cos(n^2)) =3/2
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