Use the Lagrange multiplier method to optimize the objective function 3x? + y? – 2xy subject to the constraint x + y = 6.

Q: If T : R? → R² is a linear transformation such that 7 (1) - 5 34 6 30 T and T 21 then the standard…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 - y from above inside y = x? ,y = 4.

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Q: Q3) Evaluate triple integral S dz dy dx.

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Q: Q3) Find the Area bounded by the curves y² = x and x = 2y - y?.

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin * +0) in…

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Q: QI) Evaluate the integral , S, dy dx using polar coordinate

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Q: b) Given f (x)= In x x>0. Use differentiation to find the value of f'(x) at x= 2. Give your answer…

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Q: Suppose o, p :Z → G are homomorphisms such that q(1) = 4(1). Prove o = 4.

A: Given that                      φ,ψ : ℤ→G are two homomorphisms such that φ(1)=ψ(1). To solve the…

Q: Q1. By using cubic approximation of Langrange Interpolation, approximate f(7.65) based on the…

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Q: Q2 Find the limits h +h cosh 1- lim Sinh cosh 2-lim S4ズ メ 2x-8

A: To find the limits of given . L' Hispital's Rule is

Q: There are x pink straws, 10 yellow straws, and X + 2 green straws in a bag. A straw is selected at…

A: Probability of selecting m things out of n is  p=mn

Q: Q3. Tangents are drawn from 0(0,0) to the circle x² + y² – 2x + 4y+ 1 = 0, touching the circle at L…

A: The standard form of the equation of circle is   x-h2+(y-k)2=r2   where (h,k) is center of circle…

Q: Consider the system of equations dæ = x(3 – x – 4y) dt dy = y(1 – 3æ), dt taking (x, y) > 0. dy = 0.…

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Q: 1) y" – 10y' + 25y = 8e- y(0) = 1, y'(0) = -4;

A: Follow the steps.

Q: Give an example of each of the following: • A function f e L²(T) and a point where f(x) does not…

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Q: Find a 4x4 matrix A (NON-ZERO ENTRIES ONLY) with 3 eigenvectors coming from a single eigenvalue of…

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Q: 1 2 3 4 5 6 Y 4 10 10 8 3

A: Here follow the python code.

Q: 4. 5438 + 2468 + 1438 5. 10101112 + 11010112 + 10110102 6. 1213 + 2113 + 2223

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Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) +2y 3 ,y (0) = 0,…

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Q: Solve the equation Ax = b by using the LU factorization given for A. 4 -4 4 1 0 0 4 - 4 4 - 4 A = –…

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Q: X – 1 is to be se ethod. If the ini en the absolute ation is

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Q: d. Z,Z3 + Z4 e. (Z1 + Z3)/(Z2 - Z4)

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Q: et L: M2x2 - M2x2 be the linear transformation defined by L(A) = 414, %3D or matrix A in M2x2-…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y x2,y 4.

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Q: Using implicit differentiation, find the slope of the tangent line at the point (9,16) on the curve…

A: Given curve, x+y=7 and point (9,16)

Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

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Q: The value of lim et3 -x tan x-cos x x2 is?

A: We want to find limit of given function

Q: Use Newton methad to find fis), f'ca) 9. to 3. 10

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Q: Use the Lagrange multiplier method to find the point on the surface z zy to the origin. O A. (3,3,1)…

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Q: Use a random number generator to generate five integers a, b, c, d, e, with –10 < a, b, c, d, e <10…

A: for Af continuous function  f whose  domain that includes the smooth curve CC with parameterization…

Q: The following data is provided for the velocity of an object as a function of time: 5 10 19 32 15 46…

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Q: Q4) Find plane area inside the polar function r 2 and outside polar function r=2 sin ( +e) in second…

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Q: Suppose a1, a2, a3, a4, and ag are vectors in R³, A = (a1 | a2 | a3 | a4 | a5), and [1 0 -5 5…

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin 2 + 0) in…

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Q: Is the following series convergent or divergent? Explain your answer. ex= 1+x+x2/2 + x3/6.......

A: Ratio test: A series ∑n=0∞an is convergent if limn→∞ an+1an&lt;1 and  divergent if limn→∞…

Q: Find the equation of the tangent line to the curve y = 4x-8 at the point (3.-2). Your answer

A: Curve is given y2 = 4x - 8. Slope of any curve at any point is given by dy/dx.

Q: Q2) Convert the polar function r = tan20 to cartesian.

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Q: the line integral + 2x²ydy + dz) .2,

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Q: There are six P20 peso-bills, one P50 peso- bill, and three P100 peso-bills in a wallet. If a peso…

A: We want to find probability of drawing a face value greater than 40.

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2,y 4.

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Q: Find the solution of the equation 3U,- 5U, =0 satisfying the condition U(0, y) = sin y

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Q: Suppose the position of a runner was recorded every half second and the results are given in the…

A: We are given the following table.  t 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 y 0 0.25 1 3 6 10 15…

Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e*; t = 0 T(0) = N(0)

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Q: Q: find area inside r32cose and outside r = 1?

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Q: Q1) Evaluate the integral S S dy dx using polar coordinate

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Q: Q38: If y = e2* sin 5x, then which of the following is true? e (a) y" – 4y' + 30y = 0+ - (b) y" –…

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Q: Q1) Evaluate the integral S dx dy using polar coordinate y 2-y

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Q: Hannah expects to receive Php 200,000 five years from now. How much is the money worth now if the…

A: Given Future amount = A = Php 200,000 Time = t = 5 years Interest rate = r = 10% compounded monthly

Q: Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y 4.

A: Here we can use triple integral to find the volume of the solid. Volume of a solid using triple…

Q: Q5) Find volume of body bounded by z = -y2 from below and z = x from above inside y = 0,y = x,x 1.

A: We have to find the volume of region.