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Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(1-cos4x)/(x^2)`

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`lim_(x->0)(1-cos4x)/(x^2)`
`=lim_(x->0)(2sin^2 2x)/(x^2)`
`=2lim_(x->0)((sin 2x)/(2x))^2 xx 2^2`
`=2xx1xx4`
`=8`
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