Evaluate the following limit : lim(x→0) (1 - cos mx)/(1 - cos nx)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{1-cos\,m\text x}{1-cos\,n\text x} \)

lim(x→0) (1 - cos mx)/(1 - cos nx)

Answer 1

\(\lim\limits_{\text x \to0}\cfrac{1-cos\,m\text x}{1-cos\,n\text x} \)

lim(x→0) (1 - cos mx)/(1 - cos nx)

To Find: Limits

NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form.

 In this Case, indeterminate Form is \(\cfrac00\)

Formula used : \(\lim\limits_{\text x \to 0}\cfrac{1-cos\,\text x}{\text x^2}=\cfrac12\) 

Divide numerator and denominator by m² and n² , we have

So, by using the above formula, we have