lim(∫根号(t)dt/sin(xπ),(1,x^2),x趋于1,求极限,

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lim(∫根号(t)dt/sin(xπ),(1,x^2),x趋于1,求极限,lim(∫根号(t)dt/sin(xπ),(1,x^2),x趋于1,求极限,lim(∫根号(t)dt/sin(xπ),(1,

lim(∫根号(t)dt/sin(xπ),(1,x^2),x趋于1,求极限,
lim(∫根号(t)dt/sin(xπ),(1,x^2),x趋于1,求极限,

lim(∫根号(t)dt/sin(xπ),(1,x^2),x趋于1,求极限,
原式=lim(x->1) 2x²/πcos(xπ) 利用罗比达法则
=2/π(-1)
=-2/π

lim(x→1)∫[1,x^2](t)dt/sin(xπ)
=lim(x→1)∫[1,x^2](t)dt/(π-xπ) (0/0)
=-1/π