Transcription of 3.5 Parabolas, Ellipses, and Hyperbolas - MIT …
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3.5 Parabolas, Ellipses, and Hyperbolas - MIT …
Parabolas, ellipses , and Hyperbolas 50 Define f,(x) = sin x + 4 sin 3x + f sin 5x + (n terms). Graph f5 and f,, from -x to 71. Zoom in and describe the Gibbs phenomenon at x = 0. On the graphs of 51-56, zoom in to all maxima and minima (3 significant digits). Estimate inflection points. 51 y = 2x5-16x4+ 5x3-37x2+ 21x + 683 52 y=x5-~4- JW-2 53 y = x(x -l)(x -2)(x -4) 54 y = 7 sin 2x + 5 cos 3x 55 y=(x3-2x+1)/(x4-3x2-15), -3,<x<5 56 y = x sin (llx), ,< x Q 1 57 A 10-digit computer shows y = 0 and dy/dx = .O1 at x* = 1. This root should be correct to about (8 digits) (10 digits) (12 digits). Hint: Suppose y = .O1 (x -1 + error). What errors don't show in 10 digits of y? 58 Which is harder to compute accurately: Maximum point or inflection point?
collector and a TV dish are parabolic. They concentrate sun rays and TV signals onto a point-a heat cell or a receiver collects them at the focus. The 1982 UMAP Journal explains how radar and sonar use the same idea. Car headlights turn the idea around, and send the light outward. Here is a classical fact about parabolas.
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