E2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The...
f(z) = {*3:2+1 (1:3); z = 1 Given the complex function: 1)Isf continuous on the complex plane? 2) Is fanalytic at z = (1; 0)?
14. If y =f(z) is a continuous function in a neighborhood around f'(c) = 0, does there have to be a local extrema on the graph of u = f(x) at x = c. 15. If/"(z) =-4(-7)2(z + 1) and the domain of f(x) is all real numbers, determine where f(x) is concave up, concave down and find any r-values of inflection points.
14. If y =f(z) is a continuous function in a neighborhood around f'(c) = 0, does there...
Determine the general antiderivative of the following
function:
3) f(x) = e2
This is a complex variable
question!!!!!!!!!!!!!!
Let e2 f(z) = P1-2) This function has a pole at 0. What is the order of that pole, and what is the residue Res (f;0) of that pole?
Answer C
6. Let f be a continuous function on [0, oo) such that 0 f(z) Cl- for some C,e> 0, and let a = fo° f(x) da. (The estimate on f implies the convergence of this integral.) Let fk(x) = kf(ka) a. Show that lim00 fk(x) = 0 for all r > 0 and that the convergence is uniform on [8, oo) for any 6> 0. b. Show that limk00 So ()dz = a. c. Show that lim00 So...
3. Consider the following piecewise function (a) Draw an accurate graph of f(). (b) As always, f(x), has an infinite number of antiderivatives. Consider an antiderivative F(r). Let us assume that F(r) is continuous (we don't usually have to specify this, but you will see in the bonus part of the question why we do in this case). Let us further assume that F(2) 1. Sketch an accurate graph of F(r). MATH 1203 Assignment #7-Integration Methods Due: Thurs., Apr. 4...
that f'(2) is continuous and that F(x) is an antiderivative of f(1). the following table of values: 6 f(x) F() r=0 = 2 r = 4 1 = 6 -2 1 -4 6 2. -3 5 6 -4 2 3 7 (a) Evaluate [u(z) – f(x) – 3)?f'(x)da. b) Evaluate ſz, za f'(x)dx
complex analysis
Let f(z) be continuous on S where for some real numbers 0< a < b. Define max(Re(z)Im(z and suppose f(z) dz = 0 S, for all r E (a, b). Prove or disprove that f(z) is holomorphic on S.
1) Suppose f (a, b) R is continuous. The Carathéodory Theorem says that f(x) is differentiable at -cE (a, b) if 3 (a, b)-R which is continuous, and so that, (a) Show, for any constant a and continuous function (x), that af(x) is continuous at z-c by finding a Carathéodory function Paf(x). (b) Show, for any constants a, B, that if g : (a, b) -R is differentiable at c, with Carathéodory function pg(z), then the linear combination of functions,...
κ. If / is continuous ou ¡a,bj xnd F(z) nodt, then F is differnntiable on 1, b, h. If / is integrable un la.บุ, then it has an antiderivative G on ps, bị and J 1(r) dr-G(b) i If i1 is bounded, thea (onlis converget j. If / has infinitely wauy discostinuities on Io., then f s niot integrabie on ja b. G(a)
κ. If / is continuous ou ¡a,bj xnd F(z) nodt, then F is differnntiable on 1, b,...