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Evaluate lim(xto2) sin(e^(x-2)-1)/(log(x...

Evaluate `lim_(xto2) sin(e^(x-2)-1)/(log(x-1))`

Text Solution

Verified by Experts

The correct Answer is:
1
`underset(xto2)limsin(e^(x-2)-1)/(log(x-1))=underset(t to0)lim(sin(r^(t)-1))/(log(1+t))" "["Putting "x=2+t]`
`=underset(t to0)lim(sin(e^(t)-1))/(e^(t)-1)xx(e^(t)-1)/(t)xx(t)/(log(1+t))`
`=1xx1xx1=1`
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