Consider the function f (x, y, z) = x+y+z¹ subject to the constraint x² + y² + z² = 1.

Q: 12.47. Solve the boundary-value problem J²y at2 if (a) f(x) = 4 a²y dx2¹ 5 sin , y(0, t) = y(5, t) =…

A: The given problem is to solve the given partial differential equation boundary value problem with…

Q: The plane II contains the points (1, 2, 3), (0, 1, 2) and (2, 3, 0). The line L passes through the…

A: Since you have posted a question with multiple subparts, we will provide the solution only to the…

Q: Let G be a finite semigroup. Prove that there exists e∈ G such that e = e^2.

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Q: 1. Calculate the Riemann integrals of the following functions. (a) f(2)=2²+3x+4 (c) f(z) = 42"-1/3…

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Q: Find the change of variable x = Py that transforms the quadratic form x Ax into y Dy as shown. -…

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Q: 2. (a) Let S= A 0 I B A, B & GL (R), B = B, A = (B n ¸ Check whether or not S SP2n(R). Also give an…

A: Here , I use latex to write the answer.

Q: Suppose that OABC is a parallelogram. Let M be the midpoint of OA and let P be the point of…

A: 1st we will draw diagram of the given situation and then find position of P using section formula…

Q: f(x, y) = 2x² + 9xy Local maxima are Local minima are Saddle points are m I ... ▬▬

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Q: This exercise refers to P2 with the inner product given by evaluation at -1, 0, and 1. Compute ||p||…

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Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

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Q: Given that A is a 3 by 3 matrix and the det(A) = 4. We created a new matrix B from A by switching…

A: Given that A is 3×3 matrix and det(A)= 4

Q: Let H be the hemisphere x2 + y2 + z2 = 45, z ≥ 0, and suppose f is a continuous function with f(5,…

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Q: For two finite sets A and B. prove that AUB ≤Ã+B. Prove that U [Qn (n, n+1)] is countable.

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Q: Example(4): Find the Fourier Series of the following square waveform. -A, for -T/2 <1 <-T/4 for-T/4…

A: The given problem is to find the Fourier series representation of the given periodic function of…

Q: 3. Consider the function f defined by f(x, y) = 4x² + 4y² + x² + y² − 6x²y². af af (a) Find and dx…

A: Given function  f(x,y)=4x2+4y2+x4+y4-6x2y2. Then,           ∂f∂x=8x+4x3-12xy2  and ∂f∂y=8y+4y3-12x2y

Q: Two posts, one 4 meters and the other 7 meters high, are 6 meters horizontally apart. If the posts…

A: Let us assume that x be the horizontal distance of the stake from the first post. We will use first…

Q: Define T by T: Pn → R by T(p) = =S² p(x) dx, where P is the set of all polynomials whose degree less…

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Q: Apply Green's Theorem to evaluate the integral. $(4y + x) +x)dx + (y + x)dy C: The circle (x-3)² +…

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Q: A person has a weekly salary of X dollars, and gets a raise of 16% which is worth $ 41, calculate x,…

A: Solution :- Given weekly salary = X dollars Getting raise of 16 % , which is equal to 41

Q: ∞0 11. Discuss the convergence of the series 1/n², p > 0.

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Q: 6) A homeowner is painting one coat on the side of their home which is 975 square feet, at a speed…

A: Total area to be painted is 975 square feet and speed of painting is 200 square feet per hour.

Q: Let f(x, y) = sin (x - y) [x] + [y] ' 0, |x | + (x, y)

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Q: Using either the integral or Comparison Tests, determine whether the following series converge or…

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Q: Let a be an element of a group G such that o(a) = r. Let m be a positive integer such that (m,r) =…

A: a∈GOa=rgcdm,r=1 We have to prove Oam=r

Q: The Taylor series for f(x) = x³ at -3 is Σ en(x + 3)". n=0 Find the first few coefficients. Co C1 C2…

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Q: X1 x3 = 0 = 1 3x₁ + x₂ + x3 = −x₁ + x₂ + 2x3 = 2

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Q: b) Determine the type of the given equation: xxx +(x-2)2xy + y

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Q: A curve is drawn on a sphere of radius a and the principal normal at a point P makes an angle 0 with…

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Q: Question 10. Find the Fourier cosine series forf (x) = x 72 if 0 ≤ x ≤ 1/1/0 if / ≤x≤L on 0 ≤ x ≤ L.

A: Given fx=L2        0≤x≤L2                                        0≤x≤Lx-L2    L2≤x≤LTo find:…

Q: If one of the vertices of the square circumscribing the circle |z1|= √2 is 2 + √3i, find the other…

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Q: Given, f(x)=x2-4x, [−4,8]. Find R3,L3,and M3 and give accompanying accurate sketches

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Q: If the statement is true, write a complete step-by-step proof of the state- ment. If the statement…

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Q: Evaluate the surface integral. 11. ³² ds. y² dS, S is the part of the sphere x² + y² + z² = 1 that…

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Q: The inductive step of an inductive proof shows that for k > 0, if Στo 2 = 2k+1 – 1, then Σ± 20 =…

A: Mathematical induction proof consists of two steps: 1. The base case : prove that the statement…

Q: Find the mass of a thin funnel in the shape of a cone z =√x² + y2, 1 ≤ z ≤ 3, if its density…

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Q: 7. (Chain Rule): Let ƒ : [a, b] → R, g : [c, d] → R, ƒ([a, b]) ≤ [c, d], and xo = [a, b]. If f is…

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Q: Find all the values of x such that the given series would converge. ∞ (11x)" n10 n=1 The series is…

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Q: A curve is drawn on a parabolic cylinder so as to cut all the generator. expression for curvature…

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Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t)=4e³jt f(t) may be…

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Q: 5. Draw the complete shear and bending moment diagrams. Set P = 800 lb, a = 5 ft, and L = 12 ft P P

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Q: A point is moving along the circle   in the first quadrant such that its x-coordinate changes at the…

A: The given problem is to find how fast is the y co-ordinate changing as the point passes through the…

Q: Set up the iterated double integral equivalent to (refer to the photo) bounded by the points (0,0),…

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Q: Find the radius of convergence for: 9n n x' 4" n=1

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Q: Identify four significant critiques of this chart. Draw on class instruction/discussion on…

A: Given : Chart published in a professional report on state government spending.   To solve : four…

Q: the series converges or diverges. Justify your answer. (a) Σ(n+2)(n+3) n=1 (b) For each of the…

A: We will use different test for different series  Note : Only one question is allowed to be solved at…

Q: 5) Consider the following weighted graph: 11 6 H 5 6 A 10 E 9 14 8 3 16 4 B 3 12 C Use Kruskal's…

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Q: The total cost C(q) of producing a goods is given by: What is the fixed cost? fixed cost= dollars…

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Q: 4. Use the table below to March #4 approximate the average value of g(x) using the trapezoidal rule…

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Q: Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) • Now re-parametrize…

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Q: X' = 4 -3 9- 8 X

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