Exercise 7. Let f(2)=4Re(2) and C be the line segment connecting 1+i to 0. Then the integral of f over C is equal to * O -2(1+i) O 2(1+i) O 4(1-i) O None of these
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- 21. Show that the set of polynomials {C₁, C₂ (2x - 1), C3 (6x² − 6x + 1)} in P(R) is orthogonal with respect to the inner product f f(x) g(x) dx for any choice of the constants C₁, C2, C3. For what values of c₁, C2, C3 is the set orthonormal?Abstract Algebra:Find the Selution of (1-xt +3t)4(t) de -J, (2) In which IL) denoter Bessel function.
- A small country is comprised of four states, A, B, C, and D. The population of each state, in thousands, is given in the following table. State A Population (in thousands) 53 According to the country's constitution, the congress will have 60 seats, divided among the four states according to their respective populations a) Find the standard divisor, in thousands. How many people are there for each seat in congress? standard divisor number of people for each seat (Type an integer in each box). b) Find each state's standard quota (Two of them have been done for you) State Population (in thousands) Standard quota A B C D 53 90 210 239 5.3 239 (Type an integer or a decimal rounded to two decimal places, if necessary, in each box.) c) Find each state's lower quota and upper quota Lower Quota Upper Quota State A (Type an integer in each box) State Lower Quota Upper Quota B (Type an integer in each box) State Lower Quota Upper Quota C (Type an integer in each box.) Total 600 State Lower Quota…Express the following using language of Predicate Calculus, where it is understood that the people being discussed are in the courtroom If any sentence is ambiguous, give all symbolic versions. (i) All judges are sober (ii) There is a dishonest lawyer. (iii) All defendants are innocent. (iv) Some plaintiffs are lawyers (v) Anybody who is honest and a defendant is innocent (vi) All defendants who are not sober are dishonest.4 Compute the product II (-2) j=0
- 4. Let Z[V2]= {a +b/2]a,b e Z}. Define addition and multiplication on Z[V2] as follows: (a+b [V2 ]) + (c+d [ V2 ]) = (a+c) + (b+d)[ /2] (a+b [VZ ])(c+d [/Z] = (ac+2bd) + (ad+bc) /2 Prove or disprove the following statements: (a) Z[ /2] is a ring. (b) Z[V2] is a commutative ring. (c) Z[V2] is a ring with unity. (d) Z[V2] is a field. (e) Z[ /2] is an integral domain.Compute the coefficient Fourier a, of the { T - r, 02U. Use the Fourier transform synthesis equation to determine the inverse Fourier transform of: a) X,(e*) = E {2a8(w- 2nk)+ TỔ(w- -- 2 īk) +T8(w+- 5zk)} 3 4 X, (e") = 5j for 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,