作业帮x趋近于-1,用洛必达法求,lim(1-x)^cox(πx/2)
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x趋近于-1,用洛必达法求,lim(1-x)^cox(πx/2)
lim(x->1) (1-x)^cos(πx/2)
=lim(x->1) e^[cos(πx/2)ln(1-x)]
=e^ {lim(x->1) [ln(1-x)/sec(πx/2)]}
=e^ {lim(x->1) [2cos^2(πx/2)/π(x-1)sin(πx/2)]
=e^ {1/π*lim(x->1) [(1+cos(πx))/(x-1)sin(πx/2)]}
=e^ {lim(x->1) [-sin(πx)/[sin(πx/2)+π/2*(x-1)cos(πx/2)]
=e^0
=1
=lim(x->1) e^[cos(πx/2)ln(1-x)]
=e^ {lim(x->1) [ln(1-x)/sec(πx/2)]}
=e^ {lim(x->1) [2cos^2(πx/2)/π(x-1)sin(πx/2)]
=e^ {1/π*lim(x->1) [(1+cos(πx))/(x-1)sin(πx/2)]}
=e^ {lim(x->1) [-sin(πx)/[sin(πx/2)+π/2*(x-1)cos(πx/2)]
=e^0
=1
x趋近于-1,用洛必达法求,lim(1-x)^cox(πx/2)
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