To find the correct graph for the function $y = \frac{\sin x}{x}$ for $x > 0$, we need to analyze its behavior.

Graph Analysis: $y = \frac{\sin x}{x}$ for $x > 0$

• Behavior near $x=0$: As $x$ approaches 0 from the positive side ($x \to 0^+$), the limit of the function is 1.

  $ \lim_{x \to 0^+} \frac{\sin x}{x} = 1 $

  This means the graph should start near the point $(0, 1)$.
• Behavior for $x>0$:
  • The function oscillates due to the $\sin x$ term.
  • The amplitude of the oscillations decreases as $x$ increases because of the $1/x$ factor.
  • The function crosses the x-axis (where $y=0$) when $\sin x = 0$ and $x \neq 0$. This occurs at $x = \pi, 2\pi, 3\pi, \dots$.
• Evaluating the Options:
  • Option 1: Shows oscillations, but the amplitude appears constant, not decreasing.
  • Option 2: Starts near $y=1$ as $x \to 0^+$, shows oscillations with decreasing amplitude, and crosses the x-axis at multiples of $\pi$. This matches the expected behavior.
  • Option 3: Shows oscillations with increasing amplitude.
  • Option 4: Shows a monotonically decreasing function, not oscillations.

Therefore, the figure representing $y = \frac{\sin x}{x}$ for $x > 0$ is the one showing decaying oscillations starting from $y=1$ at $x=0^+$. This corresponds to Option 2.