Transcription of 3.5 Parabolas, Ellipses, and Hyperbolas
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Example: biology
3.5 Parabolas, Ellipses, and Hyperbolas
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? First derivative or second derivative?
Quicker Solution Match the given equation with (4). Then h = 3, k = 7, and r = 2: x2 -6x + y2 -14y = -54 must agree with x2 -2hx + h2 + y2 -2ky + k2 = r2. The change to X = x -h and Y= y -k moves the center of the circle from (h, k) to (0,O). This is equally true for an ellipse: The ellipse …
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