Sketch the graph of a function f(x) with these properties: (a) Continuous on the interval (-infinity,-3) (b) Removable discontinuity at x = 3 (c) Continuous on the interval (-3,0) (d) Oscillating d For the given function ...
But if we shrink the infinite Cartesian space to a finite square, the curve dny/dxn = f(x) will have a removable discontinuity. Thus, the original curve (9) has no kink. If we rotate the coordinate system by a very small angle, the original curve (9) will be smooth formally. ...
Let f : [a, b] to R be a function which is continuous except for a simple discontinuity at x_0 in (a, b). Prove that f in R([a, b]). Prove that L(f, P) \leq U(f, P) for any bounded function f and partition P \ of \ [a, b]. ...
Give an example of a function f(x) that is continuous for all values of x except x=2 , where it has a removable discontinuity. Explain how you know that f is discontinuous at x=2 , and ho Use the definition of continuity and the properties of limits ...
How do the expansions of(x+y)nand(x−y)ndiffer? Support your explanation with an example. Expansion: Expansion is used to expand a function. One method of expansion is done by binomial expansion. Another method of expansion is Taylor's series and the Maclau...
Sketch the graph of a function f(x) with these properties: (a) Continuous on the interval (-infinity,-3) (b) Removable discontinuity at x = 3 (c) Continuous on the interval (-3,0) (d) Oscillating d Sketch a graph of a functi...