{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/41587e8a66044aaf8acec87542d1a552\" frameborder=\"0\" width=\"1840\" height=\"1380\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":1380,"width":1840,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":1380,"thumbnail_width":1840,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/41587e8a66044aaf8acec87542d1a552-0febe63008a22b0e.gif","duration":7929.147,"title":"9MA0 Set 11 Trapezium Rule and Numerical Methods","description":"In this video, I walk through solving a complex equation, demonstrating that f(x) = 0 has a root between 3.5 and 4 by evaluating f(3.5) and f(4) and observing a change in sign. I apply the Newton-Raphson method using f(4) and its derivative to find a second approximation, which results in 3.81. I also explain why the Newton-Raphson method cannot be used at x1 = 0 due to a stationary point. Additionally, I analyze a curve defined by f(x) = 8sin(0.5x) - 3x + 9 to find the x-coordinate of a local maximum and confirm the existence of a root between specific intervals based on sign changes. Please pay close attention to the calculations and reasoning presented, as they are crucial for understanding the concepts discussed."}