H.W: Use the chain rule to find the derivative of w= x² + y² with dw respect to t (dr), with x = cost+sint, y = cost - sint

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Q: 2. The Minimum point of y= 8x+4 (x-2)²

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A: let alpha and beta are in R

Q: 1. "Let fE a[a, b]. For x E (a. b), set F(x)=ff. Prove that F is continuous on [a, b].

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Q: the functions z= 8 e* Iny, x= In (u cos v), dz dz SS and- du as functions of u and v both by using…

A: Introduction: In vector calculus and differential geometry, the partial derivative is used. In…

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Q: y (0) 6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the…

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Q: Find the moment of inertia: y = x³; x = 1; y = 0 about x = -1.

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Q: II. Solve the following problems. Enclose final answer. 5. Given z arctan = (-), 5 Find az/ay

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Q: Problem 1 a. Find the Fourier transform of the given function. f(t) 2A =t+ A, ≤t≤ 0; T 2 f(t) = 0…

A: Given function is f(t)=2Aτt+A,     -τ2≤t≤0-2Aτt+A,   0≤t≤τ20,                   elsewhere Let the…

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Q: Formula valid for matrices? explain why? (A + B)(A - B) = A²B²

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Q: [2 + m 3 1. Given A= 1 a. (AB)¹ - A b. |4A-¹ + 2B-¹| a. 2AB-¹ 1 2 -1 -1 4 5+ ml and B = [-1-m 2 91 3…

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Q: Find the 103rd derivative of cos(2x).   Hint: find the first few derivatives and observe a…

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Q: 1. Given the set A = {1,2,3,4,5,6}. Given S6 = {f: A→ Alf bijective mapping} is a group with respect…

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Q: Find the approximated value of x till 6 iterations for x³-4x+9=0 using Bisection Method. Take a = -3…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

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Q: '(x) = 4x cosh 3x x² ; f'(2.7)

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Q: Find the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² 4 and the…

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Q: 6. Consider the differential equation y' = y + 2x with y(0) = 1. (a) Find a closed form of the…

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Q: 2. Find the area bounded by the two curves y = x² - 6x²+ 8x and y = x² - 4x.

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Q: X 1 4 7 9 11 f(x) 12 -23 -15 33 -13

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A: Draw and label the diagram depicting this scenario. Use law of cosines to determine the distance.

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A: Given- The relationship between training costs (x) and productivity (y) is given by the following…

Q: Q.5 Linearize the non-linear system z = x² + 4xy + 6y² in the region defined as 8 ≤ x ≤ 10, 2 ≤ y ≤…

A: Given non linear equation is z = x2 +4xy +6y2 Region :- 8≤x≤10,  2≤y≤4.

Q: 3. Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3,…

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Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

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Q: 1. Find the Laplace transform of the following function using the basic -5t definition and…

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Q: . Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x =…

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Q: use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Suppose the rule ²[ƒ(-2,−1)+4ƒ(−2,0) + ƒ(−2,1)+ ƒ (2,−1)+4ƒ (2,0)+ƒ(2,1)] applied to 12 solve f(x,y)…

A: Given: The rule, 23f-2,-1+4f-2,0+f-2,1+f2,-1+4f2,0+f2,1 is applied to solve ∫-11∫-22fx,ydxdy.   To…

Q: Find the average value of F(x,y,z)=x² + y² + z² over the rectangular solic irst octant bounded by…

A: Introduction: The formula of the average value of the function f(x,y,z) in the region E is given by,…