Evaluate limx→0sin(5x)x\displaystyle\lim_{x \to 0}\dfrac{\sin(5x)}{x}x→0limxsin(5x).A15\tfrac{1}{5}51B111C000D555check_circleExplanationRewrite: sin(5x)x=5⋅sin(5x)5x\dfrac{\sin(5x)}{x} = 5 \cdot \dfrac{\sin(5x)}{5x}xsin(5x)=5⋅5xsin(5x). As x→0x \to 0x→0, sin(5x)/(5x)→1\sin(5x)/(5x) \to 1sin(5x)/(5x)→1, so the limit is 555.