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lim(x ->0)(sin2x+sin6x)/(sin5x-sin3x)...

`lim_(x ->0)(sin2x+sin6x)/(sin5x-sin3x)`

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`lim_(xto0)((sin2x+sin6x)/(sin5x-sin3x))`
`=lim_(xto0)((2sin4xcos2x)/(2cos4xsinx))`
`=lim_(xto0)((sin4xcos2x)/(cos4xsinx)}`
`=lim_(xto0){(sin4x)/(4x)xx(r)/(sinx)xxcos2x xx(1)/(cos4x)xx4}`
`=4xxlim_(4xto0)(sin4x)/(4x)xxlim_(xto0)((x)/(sinx))xxlim_(2xto0)cos2x2xxx(1)/(lim_(4xto0)cos4x)`
`=(4xx1xx1xx1xx1xx1/1)=4.`
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