b. $\mathop {\lim }\limits_{x \to 0}\frac{1-cos3x}{1-cos5x}$= $\mathop {\lim }\limits_{x \to 0}\frac{2sin^2\frac{3x}{2}}{2sin^2\frac{5x}{2}}$= $\mathop {\lim }\limits_{x \to 0}\frac{(\frac{3x}{2})^2.(\frac{sin\frac{3x}{2}}{\frac{3x}{2}})^2}{(\frac{5x}{2})^2.(\frac{sin\frac{5x}{2}}{\frac{5x}{2}})^2}=\frac{9}{25}$
b. $\mathop {\lim }\limits_{x \to 0}\frac{1-cos3x}{1-cos5x}$= $\mathop {\lim }\limits_{x \to 0}\frac{2sin^2\frac{3x}{2}}{2sin^2\frac{5x}{2}}$= $\mathop {\lim }\limits_{x \to 0}\frac{(\frac{3x}{2})^2.(\frac{sin\frac{3x}{2}}{\frac{3x}{2}})^2}{(\frac{5x}{2})^2.(\frac{sin\frac{5x}{2}}{\frac{5x}{2}})^2}=\frac{3}{5}$
b. $\mathop {\lim }\limits_{x \to 0}\frac{1-cos3x}{1-cos5x}$= $\mathop {\lim }\limits_{x \to 0}\frac{2sin^2\frac{3x}{2}}{2sin^2\frac{5x}{2}}$= $\mathop {\lim }\limits_{x \to 0}\frac{(\frac{3x}{2})^2.(\frac{sin\frac{3x}{2}}{\frac{3x}{2}})^2}{(\frac{5x}{2})^2.(\frac{sin\frac{5x}{2}}{\frac{5x}{2}})^2}=\frac{
9}{
25}$