求lim (x→2)(x-2)tanπx/4的值

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求lim (x→2)(x-2)tanπx/4的值
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求lim (x→2)(x-2)tanπx/4的值
求lim (x→2)(x-2)tanπx/4的值

求lim (x→2)(x-2)tanπx/4的值

lim (x→2)(x-2)tanπx/4
=lim (x→2)(x-2)(sinπx/4)/(cosπx/4)
=lim (x→2)(x-2)/(cosπx/4) (罗比达法则)
=lim (x→2)1/[(-sinπx/4)π/4]
=-4/π

=lim(x->2) (x-2)*sin(πx/4)/cos(πx/4)
=lim(x->2) (x-2)/cos(πx/4)
=lim(x->2) 1/(-π/4*sin(πx/4))
=-4/π