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Evaluate lim(xto1) (a^(x-1)-1)/(sinpix)....

Evaluate `lim_(xto1) (a^(x-1)-1)/(sinpix).`

Text Solution

Verified by Experts

We have, `underset(xto1)lim(a^(x-1)-1)/(sinpix)" "`(0/0 from)
`=underset(xto1)lim(a^(x-1)-1)/(sin(pi-pix))`
`=underset(xto1)lim(a^(x-1)-1)/(x-1).underset(xto1)lim(-pi(1-x))/(pisin(pi(1-x)))`
`=log_(e)axx(-(1)/(pi))=-(log_(e)a)/(pi)`
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