EMath380 Final ExaminationO 8 https://docs.google.com/forms/d/e/1FAlpQLSdkCu0XNvRdvqKOdQwINON1kyV-9cJqTVBs1N6s2K3T-HHIUG/formRespNone of theseLet f be a function with 2 + 3i as the only singular point of it.If 2 + 3i is a removable singularity of f and C: |z - 2- 3i| = 1 then I =3Sc f(z)dz isNone of theseO by Cauchy-Goursat TheoremO but Cauchy-Goursat theorem is not applicable2+3i2njizLet f(z) =7(2)and z = 2 - i be a simple pole of f(z).25°C Partly sunny

Given f be a function with 2+3i as the only singular point of it. If f is a removable singularity of…

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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= mx + b. 4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) x + 2, and h(x) A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (−1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. =
f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X → V is injective. ) gof: X→ V is surjective. ) (gof)-¹ = f¹og-¹ v injective if x1 #xn → v(x1) = v(xn)
(4) Let f₂ = 0ƒ/əz and ƒz = 0ƒ/az. Recall f = u + iv, the notation f is used for the complex conjugate function u – iv. (e) Show that if ƒ = O(U), then A|f² = 4|f¹|².
QUESTION 1 UTM a) Find the domain and range of the function UTM &UTM 6 UTM UTM 1 UTM b) Given u = xf (2x – 3y) where f is an arbitrary function. Show that UTM UTM UTM UTM UTM з ду du 2x du UTM UTM c) A physical quantity C is given by u. UTM UTM G UTM TM UTM С (m, п, t) — 2t UTM UTM UTM UTM UTM The maximum percentage error in the measurement of m, n andt are 1%, 1.2% and 1.5% respectively. Use partial derivative to find the max- mn imum percentage error in calculating C. UTM d) A company produces two products. After considering all cost, the UTM company profit (in RM) is given by UTM UTM 1 1 -a² - y - 1 UTM 5"y + 130x + 145y – 1500, week. Determine how many product x and y should be produced per week to maximize it's profit. UTM
A function is invertible if and only if it is a bijection. True or False?
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Let V be the set of functions f: R → R. For any two functions f, g in V, define the sum f + g to be the function given by (f + g)(x) = f(x) + g(x) for all real numbers. For any real number c and any function f in V, define scalar multiplication cf by (cf)(x) = cf(x) for all real numbers . Answer the following questions as partial verification that V is a vector space. (Addition is commutative:) Let f and g be any vectors in V. Then f(x) + g(x). since adding the real numbers f(x) and g(x) is a commutative operation. (A zero vector exists:) The zero vector in V is the function f given by f(x) = for all. (Additive inverses exist:) The additive inverse of the function f in V is a function g that satisfies f(x) + g(x) = 0 for all real numbers . The additive inverse of f is the function g() for all . me for all real numbers a (Scalar multiplication distributes over vector addition:) If c is any real number and fand g are two vectors in V, then c(f+g)(x) = c(f(x) + g(x)) =
Show that there exists an x in the interval (0,1) that satisfies the given equation V = 1- x Hint: Create a function f(x) so that you can apply the Intermediate Value Theorem. MacBook Pro esc く 23 24 & 2 3 4 6 7 8 9 - Q W E R Y { S D G つ K く C V M option command command option + I" .. .- リコエリ

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Let f be a function with 2 + 3i as the only singular point of it. If 2 + 3i is a removable singularity of f and C: Iz-2-3i) - 1 then I = f(z)dz is O None of these O O by Cauchy-Goursat Theorem O 0 but Cauchy-Goursat theorem is not applicable 2+3i O2ni