3. (Analytic branches of multiple-valued functions)(a) Let w+ Vw denote the principal branch. Describe the domain of analyticity of the functionS(2) = Ve +I and find its derivative.(b) Let w Vw denote the principal branch. Describe the domain of analyticity of the functiong(2) = V – 4 and find its derivative. Is there a branch of V – 4 which is analytic on C\[-2, 2)]?

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Answered: 3. (Analytic branches of…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 8PS

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Consider a differentiable function f with domain R and derivativesf'(x)=-aebx(1+bx) and f"(x)=-abebx(2+bx) , with a and b nonzero real numbers.The function has only one critical point x=-1/b and a local maximum at x=-1/bUse the Second Derivative test to find the value(s) of a and b
1. Use the Cauchy-Riemann equation to determine if the function f(z) = x3 - i(2 - y)3 is analytic or not. Provide all the sufficient conditions and the domain of analyticity and then find the derivative if it exists.
Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x)=6*e-x , a=−0.1 Set the center of the linearization as x=0 The linearization is L(x)equals=_______________
1) The derivative of a function F (X, Y) at a point P_0 = (1,2) in the direction towards P_1 = (2,3) is 2√2,and in the direction towards P_2 = (1,0) it is -3. Find the value of the derivative at P_0 in the direction toward the origin.
Find the critical numbers of f(x) = x4(x-1)3 A. What does the second derivative test tell you about the behavior of f at these critical numbers? B. What does the first derivative test tell you?
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A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a local maximum? A local minimum?
a) Determine the domain of the function f (x) = √1 − x2. b) Calculate its derivative. Study the sign of the derivative f ′ (x) at x∈D (f). Construct a table with the sign of the derivative according to the value of x, the variations of (x) (increasing or decreasing). c) Enter in the table the value of that cancels f ′ (x), is it a minimum, or a local maximum, or absolute? Are the extremes of the domain minimum, or local maximum, or absolute?
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a) Calculate the derivative of f1 (x) = 2x4 - 3x3 + 1/2x2 + 3. b) Study the sign of the derivative f1'(x) at x ∈ ℝ by factoring f1' (x). Construct a table with the sign of the derivative according to the value of x, the variations of f1(x) (increasing or decreasing) and the limits of f1(x) at x = ± ∞. Enter in the table the values of x that cancel out f1'(x), are they local or absolute minimums or maximums? c) Calculate the equation of the line tangent to the curve: y = f1(x) at x = -1.
a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = -x2 - x + 2 on ⌊-4, 4⌋
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