Limit of \( \displaystyle \frac{\sin{\left(6 x \right)}}{2 x} \) as \( x \to 0 \)

Problem 1.131 · easy

1. \[ \lim_{x \to 0^+}\left(\frac{\sin{\left(6 x \right)}}{2 x}\right) \]
   limit algebra simplifyStart with the original limit expression. Rewrite the fraction to isolate the standard limit form. Simplify the constant coefficient.✓ Proved
2. \[ = 3 \lim_{x \to 0^+}\left(\frac{\sin{\left(6 x \right)}}{6 x}\right) \]
   limit-lawApply the constant multiple rule for limits.✓ Proved
3. \[ = 3 \]
   trig-limit simplifyUse the fundamental trigonometric limit limit_{u->0} sin(u)/u = 1, where u = 6x. Evaluate the final numerical value.✓ Proved