`lim_(x->0) (cos(mx) - cos(nx))/(x^2)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Given the limit `lim_{x->0}(cos(mx)-cos(nx))/x^2` . We have to find the limit value

Applying the limits we get,


Using L'Hospital's rule and then applying the limit we get,``


So again using L'Hospital's rule we get,


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