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Evaluate lim(xrarr0)((1-cosx))/(x^(2))....

Evaluate `lim_(xrarr0)((1-cosx))/(x^(2)).`

Text Solution

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`lim_(xto0)((1-cosx))/(x^(2))=lim_(xto0)(2sin^(2)(x//2))/(((x)/(2))^(2)xx4)`
`=1/2lim_(xto0){(sin(x//2))/((x//2))}^(2)=((1)/(2)xx1^(2))=1/2.`
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