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Evaluate: lim(x->0)(1-cosm x)/(1-cosn x)...

Evaluate: `lim_(x->0)(1-cosm x)/(1-cosn x)`

Text Solution

Verified by Experts

The correct Answer is:
`m^(2)//n^(2)`
`underset(xto0)lim(1-cosmx)/(1-cosnx)=underset(xto0)lim{(2"sin"^(2)(mx)/(2))/(2"sin"^(2)(n)/(2)x)}`
`=underset(xto0)lim[{("sin"(mx)/(2))/((mx)/(2)}}^(2)(m^(2)x^(2))/(4)xx(1)/({("sin"(nx)/(2))/((nx)/(2))}^(2))xx(4)/(n^(2)x^(2))]`
`=(m^(2))/(n^(2))`
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