Express each one of the following in the standard form a + ib. 1 A: (1 + i)? (iii) 3 - i 3+4i 1+i ||2 - 4i 3 (vi) 1- 2i - 2. V-3

Q: Prove: If S is compact, and f is continuous on S, then f takes a minimum value some- where in S.

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Q: Sketch the graphs of the following, inserting relevant values. 0 < x < 5 5 < x < 8 1 f (x) = {0 f(x+…

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Q: 80 24c 80 C = 24 Write the 80 as the product of 5 and a power of 2. Write the 24 as a factorial.…

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Q: Let M1 F → F be a transformation defined by M1(f) mation? Justify your answer. (1² + 1)ƒ(t). %3D

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Q: Sets and Events 1.4.1 As an easy exercise, check that you believe that lim [0, 1- 1/n] = [0, 1) n-00…

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Q: Solve the following integral equation using Laplace transformation t = 1+ , sin(t – u)y(u)du.

A: Laplace transferom, of integral equation

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Q: Define a sequence {E;} where En = r -,r| where n is positive integer. Find P({r}) for any r E [0,1]

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Q: f(t) = sinh? 4t cosh 4t 32s А. (s2-144)(s2-16) C. 4(s2 -144)(s2 -16) s3-4s? +560 В. (s2-144)(s2-16)…

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Q: Solve (D² + 4)y = 2 tan x ; x>0 , D= 4?

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Q: Suppose 8 people are in a race. What is the probability that Billy and Michael place 1st and 2nd…

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Q: Determine which number, 0 through 6, is the given number equivalent to in modulo 7. Write your…

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Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

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Q: 8. Let f: R-→R be a field homomorphism. Show that f is identity.

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Q: Determine the value of the following mathematical expression, where u=3 and v=6. each) 4v a. w = Зи…

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Q: Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a = e O a^4…

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Q: (За? + Зт?) da - 6атӑт —D 0 a-C = a² – m² aC = a² • 2 %3D Option 1 Option 2 С -а + т

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Q: 1. Determine the direction cosines and direction angles for à =

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Q: f(t) = sin? 4t + cos? 4t 4+s А. s2+16 C. - С. s2+32 В. s(s?+16) D. s2 +16

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Q: w1 is normal prove it prove that the first uncountable ordinal omega 1 is normal space by showing…

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Q: . Use Taylor's series, to prove that Bin z tan (x+ h)3Dtan%4 (h sin z). sin 2z +(h sin zj?. sin 3z -…

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Q: Let {xn} be a bounded sequence of real numbers. Prove that {xn} converges if and only if lim inf xn…

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Q: 1- Evaluate without a calculator. Show your work. a) Log 0.000001 b) log4 (1/16)* 33 51/4

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Q: 9. Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R…

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Q: what Is the conjugate of Js -J2i ? a. Jo -Joi d. -i b.Ja -ぶ

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Q: Express 7 (cos 300° – i sin 30°) in polar form.

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Q: 1. xy dx + (x²- 3y) dy = 0 ans. x'y = 2y + c

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