) Let z(x, y) = x" be a function defined on a disk D in the positive quadrant the point (1, 2). Prove whether z(x, y) satisfies the Clairaut Theorem containing at (1, 2).

Q: If the length of one side of a cube is 4 m. Find its Volume.

A: A Cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges in…

Q: (a) Is the function f(x, y) = xy(x²-x²) when (x, y) = (0,0) and f(0, 0) = 4 continuous at origin.…

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Q: Question 5 ( T A manufacturer assembles personal computers. If the computers are priced at £1,000…

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Q: Determine the nature and stability of the equilibrium points of the system dr = x=y+z², dt dy 12r -…

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Q: (a) Prove the convergence or divergence of each of the following series: 1! +a! +3! + +n! 20+1 2+1 6…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Q3. a) Solve the following first order differential equations, clearly showing all calculation steps…

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Q: Widget Sales Jesaki Inc. is trying to enter the widget market. The research department established…

A: Given that, The research department  of widget market established the following table,…

Q: Give a direct proof: Ifx is even, then x³ + x + 1 is odd. (Use the definitions of even and odd, and…

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Q: investor has $60,000 to invest in a $280,000 property. He can obtain either (option A) a $220,000…

A: Given: Investor=$60,000 To find: Second mortgage at 10 year

Q: (3) Find the mass of the lamina described by the inequalities, given that its density p(x, y) = xy.

A: Given,             ρ(x, y)=xy and  x≥0, 3≤y≤3+9-x2

Q: or n>3

A: Given: Mathematical statement 2Fn>Fn+1 for n>3. We have to check whether a given statement is…

Q: Let T:P2 →M be defined by T(p(t))=[p(1) p(1) p(1) p(1) p(1) p(1)], where P2 ={at2 +bt+c, where a,b…

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Q: Use the mid-ordinate rule with four intervals to evaluate the integral Type your final answer below…

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Q: Determine the validity of the following argument: (Show the three-step procedure for determining the…

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Q: 3. In fitting a parabola, the formula to find the sum of the squares of the residuals is a) E= Ey-…

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Q: 1 (t) ли И ,к≠ 0 eleccione una: . а. а = 1/2; ак b. ak ак 2кп . c. a = 0; ак . d. aj=0; ak 2кп ,к≠ 0…

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Q: Problem: A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50,…

A: We have to find the number of acres of wheat and barley to maximize the farmer's profit.

Q: 8. Explain why in any group of 1500 people there must be at least 3 people who share first and last…

A: To find- Explain why in any group of 1500 people there must be at least 3 people who share first and…

Q: (a) Assume that g(x, y) is a function of the form g(x, y) {} 0 if (x, y) = (0,0). (i) Show that…

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Q: Let T:P2 →M be defined by T(p(t))=[p(1) p(1) p(1) p(1) p(1) p(1)], where P2 ={at2 +bt+c,where a,b…

A: Given : T : P2 → M  defined by ;   Tp(t) = p(1)p(1)p(1)p(1)p(1)p(1) ,  where  P2 = at2+bt+c : a, b,…

Q: Evaluate the following integral by reversing the order of intgeration: √ 2π [²² 1²² cos(7x²) dxdy…

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Q: Q2: Use bisection to determine the drag coefficient needed so that an 80-kg parachutist has a…

A: Solution :-

Q: Suppose G(r) is the generating function of a sequence (an), satisfying G'(r)=rG(r), G(0) = 1. iii.…

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Q: 4. Prove that a permutation matrix is orthogonal.

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Q: umeral for the Roman n

A: Introduction: Manuscript numerals are a symbolic representation of numbers that do not have a place…

Q: 1 0 3 7 10 12 (days) r(1) (centimeters per day) -6.1 -5.0-4.4 -3.8 -3.5 4. An ice sculpture melts in…

A: According to intermediate value theorem if a continuous function, f, with an interval, [a, b], as…

Q: Show that the interval of convergence of the series n=1 1 << √2 √2 27-12-1 (4n - 3)² is given

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Q: 3. Find the fixed point(s) of f: [1, ∞)→→ [2, ∞) defined by f(x) = √²+x.

A: 3) To find: fixed points of f:[1,∞)→[2,∞) defined as f(x)=x2+x.

Q: Date Title Page No. Teacher Sign / Remarks find the smallest prime number dividing the Sum 3+ 5 ¹13

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Q: Calculate the 4th roots of (5 - j3)

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Q: Explain how to solve difference equations using the iterative method.

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Q: 1. The set of all pairs of real numbers of the form (x, 0) with the standard operations on R2.

A: 4. Given that the set of all pairs of real numbers of the form (x, 0) with the standard operation on…

Q: Let f and g be real-valued continuous functions in the vector space C[a, b]. Show that (f. g) =…

A: Given that f and g be real-valued continuous function in the vector space Ca,b. We have to show that…

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: Maximize z = 8x + 2y, subject to the following constraints. (If an answer does not exist, enter…

A: Given the equation: z=8x+2y constraints: 2x-5y≤10; -2x+y≤2; x≥0; y≥0   To find the maximum value of…

Q: 2.Show that (P 'n Q) V (Q 'n P) is a Tautology.

A: To Show- Show that P' ∧ Q ∨ Q' ∧ P is a Tautology.

Q: Analyze the given system for b > 0, (fixed points, stability, bifurcation point, limit cycle, etc.).…

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Q: 4. Let S = {a, b, c, d, e, f, g, h} and T = {b, c, d, f,i,j}. a) List the entries of the set S-T,…

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Q: 3. Recall that Km,n denotes a complete bipartite graph on (m, n) vertices. a. Draw K4,2- b. Draw…

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Q: Solve each system + y +2= y +14: x + 2y x a) (3x 11 non 11 6 = -5 (2x + b) 3x + y +2: = 3y + " 11 17…

A: We need to solve the system of equations given in part a) and b) We will use elimination method to…

Q: Consider the statement for your answers in numbers 11 and 12. Given: A,, C,and D are collinear in…

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Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x-1 for 2 ≤ x ≤ 3. Prove that f(x) is…

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Q: Exercise 4. For the function f(x) = x² + 2x² + 4x₁ + 4x2 prove by induction that the method of…

A: Solution : Given, f(x)=x12+2x22+4x1+4x2 ∇f(x)=2x1+44x2+4 ∇2f(x)=2004&gt;0 Applying method of…

Q: Note: - d= -²-1 (a) Ti You are attempting question 4 out of 12 C:= = 4 equal to,

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Q: Find each indicated measure for 0. 37. m/LEOF 38. mEJH 40. m/FOG 41. m/EG 39. mFH 42. m/IF} 70

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Q: (@) Let FOR^ → R be a Function given by F(x₁, x,...,xn) = x²₁².. X²...x² x², where ) > x ²₁ =1. Show…

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Q: If the Laplace transform of a function f is defined and denoted by F(p), find an expression for the…

A: The solution is given as

Q: Solve the initial value problem. -1 1 0 y' 1 -1 -2 y, y(0) -1 -1 -1 6 5 -7

A: This is a problem of system of differential equation.

Q: 4. In Chebyshev polynomials form, the value cos 20 = ... a) (T₂(x) + T₁ (x)) c) (T₂(x) - T₁(x))) b)…

A: Chebyshev polynomial Tn(x) of the first kind is a polynomial in x of degree n defined for x=cos…