作业帮设f(x)=(1-X)tan兀x/2,X∈(0,1],补充定义f(1)=___时,可使f(X)在[0,1]上连续.
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![设f(x)=(1-X)tan兀x/2,X∈(0,1],补充定义f(1)=___时,可使f(X)在[0,1]上连续.](/uploads/image/z/7835123-11-3.jpg?t=%E8%AE%BEf%28x%29%3D%281-X%29tan%E5%85%80x%2F2%2CX%E2%88%88%280%2C1%5D%2C%E8%A1%A5%E5%85%85%E5%AE%9A%E4%B9%89f%281%29%3D___%E6%97%B6%2C%E5%8F%AF%E4%BD%BFf%28X%29%E5%9C%A8%5B0%2C1%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD.)
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设f(x)=(1-X)tan兀x/2,X∈(0,1],补充定义f(1)=___时,可使f(X)在[0,1]上连续.
设f(x)=(1-X)tan兀x/2,X∈(0,1],补充定义f(1)=___时,可使f(X)在[0,1]上连续.
设f(x)=(1-X)tan兀x/2,X∈(0,1],补充定义f(1)=___时,可使f(X)在[0,1]上连续.
即需在x=1左连续
即
f(1)=lim x->1- f(x)
=lim x->1- (1-x)tan(pi*x/2)
=lim x->1- (1-x)/cot(pi*x/2)
0/0型,洛必达
=lim x->1- (-1)/(-csc^2(pi*x/2)*pi/2)
=2/pi