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Evaluate: lim(xto0)(int(0)^(x^(2))cos^(2...

Evaluate: `lim_(xto0)(int_(0)^(x^(2))cos^(2)tdt)/(xsinx)`

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Verified by Experts

The correct Answer is:
`1`
Given limit is of the form `0/0`.
Then by L'Hopital's rule.
Given limit `lim_(xto 0) (int_(0)^(x)cos t^(2)dt)/x =lim_(xto 0) (cosx^(2))/1=1`.
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
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