用无穷小替换 lim x趋向无穷 (2x^2 - 1)/(X^3+x-1)的整体乘(arctanx+cosx+1)
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用无穷小替换 lim x趋向无穷 (2x^2 - 1)/(X^3+x-1)的整体乘(arctanx+cosx+1)
![用无穷小替换 lim x趋向无穷 (2x^2 - 1)/(X^3+x-1)的整体乘(arctanx+cosx+1)](/uploads/image/z/1844412-60-2.jpg?t=%E7%94%A8%E6%97%A0%E7%A9%B7%E5%B0%8F%E6%9B%BF%E6%8D%A2+lim+x%E8%B6%8B%E5%90%91%E6%97%A0%E7%A9%B7+%282x%5E2+-+1%29%2F%28X%5E3%2Bx-1%29%E7%9A%84%E6%95%B4%E4%BD%93%E4%B9%98%EF%BC%88arctanx%2Bcosx%2B1%EF%BC%89)
lim(x->∞) (2x^2 - 1) /(x^3+x-1) = 0
x->+∞,arctanx ->π/2 ; x->-∞,arctanx -> -π/2
当x->∞时,(arctanx+cosx+1)为有界函数,
无穷小与有界函数的乘积还是无穷小,于是
lim(x->∞) 【(2x^2 - 1) /(x^3+x-1) *(arctanx+cosx+1)】= 0
x->+∞,arctanx ->π/2 ; x->-∞,arctanx -> -π/2
当x->∞时,(arctanx+cosx+1)为有界函数,
无穷小与有界函数的乘积还是无穷小,于是
lim(x->∞) 【(2x^2 - 1) /(x^3+x-1) *(arctanx+cosx+1)】= 0
用无穷小替换 lim x趋向无穷 (2x^2 - 1)/(X^3+x-1)的整体乘(arctanx+cosx+1)
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