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Cyclic errors, in manufacturing, 293 Cycloidal curve acceleration, maximum, in, 103 characteristics of, 76, 77f 78f in dwell-rise-dwell cam, 44 46, 44f, 45f, 50t, 52f, 58t in dwell-rise-return-dwell cams, 53, 53f, 78 81, 80f dynamic characteristics of, 404f, 405 factors for, 553t harmonic content, 103 high-speed systems and, 448 modi ed with parabolic curve, 61 70, 62f, 68f, 78 81, 80f Wildt curve, 76 78, 79f segment characteristics, 83f shaft windup in, 383, 383f, 384f spring forces and, 223, 224f torque in, 230, 231f transient-response curves, 362, 363, 363f, 365f, 389, 390f, 391f vibratory response in, 400 Cylindrical blade cam, 10, 11f Cylindrical cams, 9 10, 10f elastic contact theory for, 255, 256f in intermittent motion mechanisms, 484 485, 485f D Alembert s principle, 219 Damping dynamic response spectra and, 401 403 modeling of, 342 348 dry (Coulomb) friction, 344 345 equivalent dampers, 346 348 mechanical ef ciency, 345 346 reasons for including, 342 values in, determining, 342 343 viscous (speed-dependent) damping, 343 344 natural frequencies and, 320 Damping coef cient, 343 D-Curve, 102, 405f, 406f Deep reactive ion etching (DRIE), 510 Deep-vertical lithography, 510 DESINE software, 537, 540, 541, 563 Diesel intake valve curves, 536, 538f Discontinuities in acceleration curves, 30, 296 297, 297f, 400, 448 449 in basic curves, 29 B-splines and, 109, 110, 132

In the program, notice that each extension method is contained in a static class called MyExtMeths As explained, an extension method must be declared within a static class Furthermore, this class must be in scope in order for the extension methods that it contains to be used (This is why you needed to include the SystemLinq namespace to use the LINQrelated extension methods) Next, notice the calls to the extension methods They are invoked on an object, in just the same way that an instance method is called The main difference is that the invoking object is passed to the first parameter of the extension method Therefore, when the expression

valAbsDivideBy(-2)

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Disk cam, 7 contact stresses in, 258 259, 259f double-disk, 8 9 Displacement in automotive cams, 536, 537f, 538f in combining curves, 57, 63 in constant acceleration curve, 34 36, 35f, 50t, 51f skewed, 37f, 38 in constant velocity curve, 33, 33f, 50t in cubic no 1 curve, 39, 50t, 51f in cubic no 2 curve, 40, 50t, 51f in curve factor calculations, 551 in cycloidal curve, 45, 45f, 50t, 52f, 77f, 83f de nition of, 30 in dwell-rise-dwell curves, general derivation, 94 96 in elliptical curve, 48, 49f equation for, 28, 62 in harmonic curve double, 46, 46f, 50t, 51f simple, 42 44, 42f, 50t, 52f, 82f in polynomial curves eighth degree, 84f simple, 32 in polynomial equation, 90 in sine curve, modi ed, 73, 73f, 75 76, 77f in trapezoidal curve modi ed, 61 70, 62f, 68f, 77f skewed modi ed, 70 73, 71f, 72f Displacement diagrams, 17 18, 17f DOCTOR DOCTOR software, 540, 541, 563 Double-disk cams, 8 9 Double harmonic curves in dwell-rise-dwell cam, 46, 46f, 50t, 51f in dwell-rise-return-dwell cams, 53, 53f spring forces and, 223, 224f DRD See Dwell-rise-dwell cam DRDRD See Dwell-rise-dwell-return-dwell cam DRIE (deep reactive ion etching), 510 DRRD See Dwell-rise-return-dwell cam DRS See Dynamic response spectra Drum cam, 9 Dry (Coulomb) friction, 344 345 Dwell in 2-3-polynomial curve, 91f in 3-4-5 polynomial curve, 92f de nition of, 15 error during, 295 variable, 472, 473f

SOLUTION As x 0 both numerator and denominator tend to zero, so the quotient is indeterminate at 0 of the form 0/0 Thus l H pital s Rule applies Our limit equals (d/dx)x 3 , x 0 (d/dx)(x sin x) lim provided that this last limit exists It equals 3x 2 x 0 1 cos x lim This is another indeterminate form So we must again apply l H pital s Rule The result is 6x lim x 0 sin x This is again indeterminate; another application of l H pital s Rule gives us nally 6 = 6 x 0 cos x lim We conclude that the original limit equals 6 You Try It: Apply l H pital s Rule to the limit limx 0 x/[1/ ln |x|] Indeterminate Forms Involving We handle indeterminate forms involving in nity as follows: Let f (x) and g(x) be differentiable functions on (a, c) (c, b) If

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