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Evaluate: ("lim")(xvecpi/2)(1+cos2x)/((p...

Evaluate: `("lim")_(xvecpi/2)(1+cos2x)/((pi-2x)^2)`

Text Solution

Verified by Experts

`underset(xto(pi)/(2))lim(1+cos2x)/((pi-2x)^(2))" "`(0/0 from)
`underset(hto0)lim(1-cos(pi-2x))/((pi-2x^(2)))=underset(xto(pi)/(2))lim(2sin^(2)((pi)/(2)-x))/(4((pi)/(2)-x)^(2))`
`=1/2(underset(xto(pi)/(2))limsin((pi)/(2)-x)/(((pi)/(2)-x)))^(2)`
`1/2`
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