Question

evaluate lim as x goes to 0 of sin(14x)/tan(5x)? evaluate lim as x goes to 0 of sin(14x)/tan(5x)? @Mathematics

Answer 1

\[\lim_{x \rightarrow 0}\frac{\sin(ax)}{\tan(bx)}\]
\[\lim_{x \rightarrow 0}\frac{\sin(ax)}{\frac{\sin(bx)}{\cos(bx)}}\]
\[\lim_{x \rightarrow 0}\frac{\sin(ax)}{\frac{\sin(bx)}{\cos(bx)}} \cdot \frac{\frac{1}{ax}}{\frac{1}{ax}} \cdot \frac{\frac{1}{bx}}{\frac{1}{bx}}\]
\[\lim_{x \rightarrow 0}\frac{\frac{\sin(ax)}{ax}}{\frac{sin(bx)}{bx \cos(bx)}} \cdot \frac{1}{\frac{1}{ax}} \cdot \frac{\frac{1}{bx}}{1}\]

Answer 2

\[\lim_{x \rightarrow 0}\frac{\frac{\sin(ax)}{ax}}{\frac{\sin(bx)}{bx}} \cdot \frac{\frac{1}{bx}}{\frac{1}{ax}} \cdot \frac{1}{\frac{1}{\cos(bx)}}\]

Answer 3

\[\frac{1}{1} \cdot \frac{1}{b} \cdot \frac{a}{1} \cdot \frac{1}{\cos(0)}\]

Answer 4

\[\frac{a}{b}\]