limx→π2lnsinx(2x−π)2．

Question

lim

x→(π)/(2)

(lnsinx)/((2x−π)2)．

Answer 1

lim

x→(π)/(2)

(lnsinx)/((2x−π)2)（(0)/(0)型未定式）
=

lim

x→(π)/(2)

(cosx)/(4sinx(2x−π))（(0)/(0)型未定式）
=

lim

x→(π)/(2)

(−sinx)/(4cosx(2x−π)+8sinx)
=−(1)/(0+8)＝−(1)/(8)