两道高数求极限的题,同济第六版,用图上提示的方法做,快考试了帮忙解答一下呗~谢啦
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两道高数求极限的题,同济第六版,用图上提示的方法做,快考试了帮忙解答一下呗~谢啦
![两道高数求极限的题,同济第六版,用图上提示的方法做,快考试了帮忙解答一下呗~谢啦](/uploads/image/z/5717027-11-7.jpg?t=%E4%B8%A4%E9%81%93%E9%AB%98%E6%95%B0%E6%B1%82%E6%9E%81%E9%99%90%E7%9A%84%E9%A2%98%EF%BC%8C%E5%90%8C%E6%B5%8E%E7%AC%AC%E5%85%AD%E7%89%88%EF%BC%8C%E7%94%A8%E5%9B%BE%E4%B8%8A%E6%8F%90%E7%A4%BA%E7%9A%84%E6%96%B9%E6%B3%95%E5%81%9A%EF%BC%8C%E5%BF%AB%E8%80%83%E8%AF%95%E4%BA%86%E5%B8%AE%E5%BF%99%E8%A7%A3%E7%AD%94%E4%B8%80%E4%B8%8B%E5%91%97%7E%E8%B0%A2%E5%95%A6)
lim(x->∞)[x^2(1-xsin(1/x))]
=lim(x->∞)[x^3(1/x-sin(1/x))]
=lim(x->∞)[(1/x-sin(1/x))/(1/x)^3]
=lim(t->0)[(t-sint)/t^3] (令t=1/x)
=lim(t->0)[(1-cost)/(3t^2)] (0/0型极限,应用罗比达法则)
=lim(t->0)[sint/(6t)] (0/0型极限,应用罗比达法则)
=(1/6)lim(t->0)(sint/t)
=(1/6)*1 (应用重要极限)
=1/6;
lim(x->0)[(tanx-sinx)/(ln(1+x^2)*sinx)]
=lim(x->0)[tanx(1-cosx)/(ln(1+x^2)*sinx)]
=lim(x->0)[secx(1-cosx)/ln(1+x^2)] (分子分母同除sinx)
={lim(x->0)(secx)}*{lim(x->0)[(1-cosx)/ln(1+x^2)]}
=1*{lim(x->0)[(1-cosx)/ln(1+x^2)]}
=lim(x->0)[(1-cosx)/ln(1+x^2)]
=lim(x->0)[sinx/(2x(1+x^2))] (0/0型极限,应用罗比达法则)
=(1/2)lim(x->0)[(sinx/x)/(1+x^2)]
=(1/2)[lim(x->0)(sinx/x)]/[lim(x->0)(1+x^2)]
=(1/2)*1/(1+0^2) (应用重要极限)
=1/2。
再问:![](http://img.wesiedu.com/upload/6/86/686f94f50df057affc727b9fd2127a4e.jpg)
再问: 大神能不能帮忙解答下刚发过去的照片上这个小题,谢谢了!!
再答: 你这题有问题,无法解答。好像是抄写错误。
再问: 好吧==!谢谢~
=lim(x->∞)[x^3(1/x-sin(1/x))]
=lim(x->∞)[(1/x-sin(1/x))/(1/x)^3]
=lim(t->0)[(t-sint)/t^3] (令t=1/x)
=lim(t->0)[(1-cost)/(3t^2)] (0/0型极限,应用罗比达法则)
=lim(t->0)[sint/(6t)] (0/0型极限,应用罗比达法则)
=(1/6)lim(t->0)(sint/t)
=(1/6)*1 (应用重要极限)
=1/6;
lim(x->0)[(tanx-sinx)/(ln(1+x^2)*sinx)]
=lim(x->0)[tanx(1-cosx)/(ln(1+x^2)*sinx)]
=lim(x->0)[secx(1-cosx)/ln(1+x^2)] (分子分母同除sinx)
={lim(x->0)(secx)}*{lim(x->0)[(1-cosx)/ln(1+x^2)]}
=1*{lim(x->0)[(1-cosx)/ln(1+x^2)]}
=lim(x->0)[(1-cosx)/ln(1+x^2)]
=lim(x->0)[sinx/(2x(1+x^2))] (0/0型极限,应用罗比达法则)
=(1/2)lim(x->0)[(sinx/x)/(1+x^2)]
=(1/2)[lim(x->0)(sinx/x)]/[lim(x->0)(1+x^2)]
=(1/2)*1/(1+0^2) (应用重要极限)
=1/2。
再问:
![](http://img.wesiedu.com/upload/6/86/686f94f50df057affc727b9fd2127a4e.jpg)
再问: 大神能不能帮忙解答下刚发过去的照片上这个小题,谢谢了!!
再答: 你这题有问题,无法解答。好像是抄写错误。
再问: 好吧==!谢谢~