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Evaluate lim(xto0) {(sinx-x+(x^(3))/(6))...

Evaluate `lim_(xto0) {(sinx-x+(x^(3))/(6))/(x^(5))}.`

Text Solution

Verified by Experts

The correct Answer is:
`1//120`
`underset(xto0)lim(sinx-x+(x^(3))/(6))/(x^(5))=underset(xto0)lim(x-(x^(3))/(3!)+(x^(5))/(5!)-(x^(7))/(7!)+* * *-x+(x^(3))/(6))/(x^(5))`
`=underset(xto0)lim((1)/(5!)-(x^(2))/(7!)+...)=(1)/(120)`
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