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Evaluate lim(xto (pi^(-))/(2)) (cosx)^(c...

Evaluate `lim_(xto (pi^(-))/(2)) (cosx)^(cosx).`

Text Solution

Verified by Experts

Let `y=underset(xto (pi^(-))/(2))lim(cosx)^(cosx)" "(0^(0)" form)`
`:." "logy=log underset(xto (pi^(-))/(2))lim(cosx)^(cosx)`
`=underset(xto (pi^(-))/(2))limlog[(cosx)^(cosx)]`
`=underset(xto (pi^(-))/(2))lim(log(cosx))/(secx)`
`=underset(xto (pi^(-))/(2))lim((-sinx)/(cosx))/(secxtanx)" "`(Using L'Hospital's rule)
`=underset(xto (pi^(-))/(2))lim(-cosx)=0`
`:." "y=1`
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