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Q: COMPLEX ANALYSIS Please answer all questions Let F be the branch of log z, which is analytic in the…

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Q: fr (3x - y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² Evaluate…

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Q: a. Show that if a, b, c, de Zwith a +b√2 = c+d√2, then a = c and b=d. You may use, without proof,…

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Q: COMPLEX ANALYSIS QUESTION PLEASE ANSWER ALL QUESTIONS DERIVATIVES Let f be a function whose domain…

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Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: Write the following system of equations as matrix equations Ax=b and solve the computing A-¹b.…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: If F(r) 17r 3 and o is the surface (x − 4)² + y² + z² = 49 oriented ||r||³ outwards, what is the…

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Q: Show that if m and b are fixed (but unspecified) real numbers then the function f(x) = mx + b is…

A: A function f(x) is said to be continuous at a point x=a, in its domain if the following three…

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A: Annual gross income is the total amount that an employee receives from a company in one years after…

Q: 3. Let f(x)=x² + 3 and g(x)=x³-1. Use the standard inner product on C[0, 1] to compute the…

A: An inner product space on the vector space V over the field F is a map from V×V to F written as  , .…

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Q: ifferen 1) y =

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Q: Suppose f(2)= 0 anz" is entire. in=0 If |ƒ(z)| ≤ 3|z|ln(|z| + 1) for all z, prove that f is a…

A: Given: fz=∑n=0∞anzn is entire. fz≤3zlnz+1 for all z. To prove: f is a polynomial.

Q: Find all the values of 0, if 0 is in the interval [0°, 360°) and has the given function values. 1)…

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Q: Exercise 11. For what values of p is the function f(x) = { {JzP sin (!) x #0 x = 0 0 differentiable?

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Q: 60 - B = ๘ ๘

A: Given cosθ = 22

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Q: Two friends wash cars to make extra money. The profit P(x) of one friend after x days can be…

A: Given that profit P(x) of one friend after x days can be represented by the function P(x) = - x ^ 2…

Q: Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the…

A: Given the function is fx=2+sinx, 0≤x≤π Here a=0, b=π

Q: Evaluate the determinant. 2       14      3      1 1        5       -1     3 1        -2       2…

A: Determinant of the matrix  Determinant of the matrix exist only if the matrix is square matric  It…

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Q: Prove that (C, +) ≈ (R × R, +).

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = 2

A: This is a problem of differential geometry.

Q: Let G(x) = [² w(t) dt. -2 Find a function, w, and a number, a, such that G(x) = 4x−² – 1. w(x) = a "

A: Evaluation of the integral

Q: Prove or disprove: Every tree has at most one perfect matching.

A: We use mathematical induction to solve this problem. The detailed solution is typesetted in latex…

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. 3 4 49

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Q: For fems 11 – 15. Refer to the figure below. Given: m || u and Q || L 13 9 10 5 1 6 15 2 12 8 4 m' u…

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Q: Suppose f(2) = If f(z)| ≤ 3|2ln(|z| anz is entire. + 1) for all z, prove that f is a polynomial.

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Q: 3. 2x₁ - x₂ 2 X x, - 3x2 + X3 = -2 -X, + X2 - 3x3 = -6 ||

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Q: 3. Let p and q be the statements Express each of these a.) p q b.) ~pv (p^q) p: I bought a lottery…

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Q: B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ and M₂. Each…

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Q: (a) Show that (Coo || • ||…) is not complete.

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Q: COMPLEX ANALYSIS Please answer all questions Let g(x, y) = y (a) Show that g is harmonic in D = {(x,…

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Q: 13. Let g: R2 → R be a function given by xy x+y g(x, y) = { 0; if (x, y) = (0,0) (a) Show that g(x,…

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Q: Compute ffs FdS for F = where S surface of the olid region bounded on the "side" by the cylinder x²…

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Q: Let a and b two positive integers. Then we have that axb LCM(a,b) = GCD(a,b). O True O False

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Q: f(x) = e²x cos(x)

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Q: 7. Polly purchased a car. She paid P150,000 as down payment and pays P5,500 at the end of each month…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² − 8)i + tj; t = 8 - T(8)= N(8) = =

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Q: Compute the product of C(90°)B(180°)A(−90°) using the points A(6,2), B(1, 2) and C(6,-3). What are…

A: Given: The product of rotations, C90°B180°A-90° and the points A6,2, B1,2 and C6,-3.   To determine:…

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Q: 6. Write each of the propositions in the form "p if and only if q": a.) For you to get a passing…

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Q: A periodic function f(x)=f(x+27) is given by -7≤X<0 2 f(x)= A-X , 0≤x≤a 2 (a) Sketch f(x) and state…

A: The graph of an even function is symmetrical around the y-axis. The graph is symmetrical around the…

Q: 14. (i) Describe the system of planes (A diagram may be helpful). (ii) Solve the system if possible.…

A: Given the system of equations as 6x-4y+2z=72x+y-4z=3-15x+10y-5z=354 so, we have to solve this system…

Q: Let f a function that allows continuous second partial derivatives: Vf(x, y) = (x³ - ax², y² - ay)…

A: Let us consider the given function z=f(x,y) Determine D(x,y)=fxxfyy-(fxy)2 The maxima/minima is…

Q: At what interest rate will a principal of P9,500 accumulate to P15,000 in 2 years noounded…

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Q: Let B be an ordered basis for R² and linear transformation to be "identity transformation" L(v) = V…

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Q: 13. Find the mass of a thin funnel in the shape of a cone z = √√x² + y², 1 ≤ z ≤ 4, if its density…

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