If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

Q: x¹ + x² + 1 I(x² + 1)² -dx.

A: The given integral is: ∫x4+x2+1xx2+12dx Evaluate the given integral.

Q: 6. The graph of the function y = x¹ is transformed to the graph of the function y=-[2(x+3)]¹ + 1 by…

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Q: 11: Given the function f(x) = 8x² - 4x₁x₂ + 5x² and Xo = [5 2]. Then G¹g at Xo is equal (( G is the…

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Q: Prove that G = {a+b√2: a, b € Q and a and b are not both zero} is a subgroup of R* under the group…

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Q: The particular solution of the differential equation y" + 2y′ − 3y = 5e²x (Select one) a) yp = e²x…

A: Here we can use operator method to find the particular solution of the differential equation. In…

Q: temperature T of a heated circular plate with the origin being at the center 64 T(x, y) = * x² + y²…

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Q: Consider the function Ha(x) defined on [0, π] as Ha(x) = a 0 and as t → 0.

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Q: The Hessian matrix for f(x) = x³x3 + x2x3 at the point [1 2 3] is given by: [6 0 31 [18 0 31 [3 0 6]…

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Q: 5: The Hessian matrix for f(X) = x}xy + x3x3 at the point (1 2 3], is given by: [6 0 31 [3 0 61 [18…

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Q: If u(x.y) and v(x.y) are differentiable, than, is it necessary that f(z)=u(xy)+iv(x.y) is also…

A: We know complex numbers are of the form ,  z = x + i y. Here , x = Real part of complex number  and…

Q: what is the difference between Binet's formula to its simplified version? Are there any rules on…

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6). please solve in steps…

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Q: 14 Across: uxx + ux + uy - 0 is a ______differential equation.

A: The given Partial differential equation is uxx+ux+uy-0. To find: the type of given Partial…

Q: 12: Apply Newton's method with line search for f(x) = x₁-x2 + 2x² + 2x₁x₂ + x2 with a starting point…

A: We have f(X) = x1-x2+2x12+2x1x2+x22

Q: One section of a suspension bridge hangs between two towers that are 50 feet above the surface and…

A: To find: The equation of the parabola that is shown in the given figure.

Q: Determine the first root of the function f(x) = -13 - 20x + 19x²-3x³ with (a) bisection method, and…

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Q: 1. Rotation 180° clockwise about the origin 3 A J →X

A: The linear transformation is very useful in different types of transformation. The important kinds…

Q: Q2. Find the angle between the vectors and .

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Q: 3: The cubic interpolation method with two points has converge rate with order three. True False

A: Solution

Q: Construct a kite ABCD having AB of length 50 mm, BC = 80 mm, and angle BAD = 55°. Measure BD and…

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Q: ces adding in order as 1-0,1-2, 2-0, 2-3 and 3-1

A: KRON node elimination technique is the direct determination of the Zbus matrix without forming the…

Q: -31 B -9 .The QR factorization of -6 [/²/3 - 1/√√/2] 3√√2 = ] 0 2 - 1/2 √2) (a) Applying the QR…

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Q: o q Lor -00 10 The function determining the shapes above is f(x) = a√z. The area shown on the first…

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Q: Use substitution to find the general solution of the system x₁ = 3x₁ + 7x2, x2 = 3x1 - 1x2.

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Q: -31 B -9 .The QR factorization of -6 [/²/3 - 1/√√/2] 3√√2 = √2 2 0 - 1/2 √2) (a) Applying the QR…

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Q: Recall that the general solution to the following boundary value problem for the heat equation Ut =…

A: Note that: the solution for heat equation exponential part is negative, where as your solution is…

Q: 3. Find the inverse of the matrix A = 1 0 -2 2 4] 1 3 2, if it exists. 5

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Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: The polar equation r(0) = 4 + 5. sin(0) is graphed below. 15- 14 13- 12 11 10- 9 8 7 6 5 O 4 3 2 10…

A: Please see the type syntax

Q: why is the topologist's comb connected but not path-connected?

A: Introduction: Every path-connected space is connected locally. If and only if it is connected, a…

Q: 24 -5-3 If R = and C= -3 1 64 and hence solve the matrix equation R = CS. find the inverse of C

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Q: Find the volume and the dimensions of the largest rectangular box in the first octant with three…

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Q: * Consider the following matrices /1 1 1/2 3 4) ^ - (-: 2) - - († ;) -- ( 7² :¦ ¦) -- () --(:::;) A…

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Q: 11. Which of these tax forms reports an employee's yearly wages, tips, and other compensation? W-2…

A: We have to find the correct choice.

Q: mod can be applied if the function is continuous only.

A: We have to check whether the Fibonacci method is applied if the function is continuous only.

Q: Q4. Find dz/dt where z = 2xy - x² y² and x = 2t, y = t²

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Q: Find the differential equation such that y(x) = c₁(x-4)³ + c₂! 64x² d²y + +60x+y=0 dx² dx 64(x-4)²…

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Q: 19 Across: The equation ut  = uxx is commonly called the __________ equation.

A: We will use basic definitions of pde

Q: 3. Determine the center and radius of the following sphere: x² + y² + z² - 2x - 4y + 8z - 15 = 0

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Q: 9 * Q3 B: Determine the - distance (S) to which the 90 kg painter can climb without causing the 4 m…

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6).

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Q: *Consider the following matrices 3 A=(-₂3³) B-(²5) C- (1²82) B= C= D (1)-( : ) E 0 1 0 9 30 2, (a)…

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Q: Let 21 = 8(cos(190°) + i sin (190°)) and Z2 17(cos(14°) + i sin(14°)). = Compute each of the…

A: If z = r e^(i x) implies z = r ( cos (x) + i sin (x))

Q: I Use the bisection method to find p3 for f(x) = r - 16 2 on [0, 1]. 0 0100 نت | حظر 3 ده | د |- 4 د…

A: To reach the exact root halving the interval in each step. P3 is the third approximate step.

Q: 14: Given three vectors u = [1 0 0], v= [1 0 -3]" and w= [1 -3 -5]". Which of the following matrix…

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Q: Find the determinant of by cofactor expansion. 5 0 7 0 1 -7 -8 - 4 0 0 0 0 0 6 3 0 -20 4 1 0 0 - 5 0…

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Q: (a) Given functions f(x) = 3x +2 and g(x) = x3³ - 1, find fog and the inverse of fog. 4. (b) Use the…

A: To solve the given problems :-

Q: - What is the second derivative of the function f(x) = xex ? What is the coefficient of the third…

A: solution is given below:

Q: = AY with A = ').L dt 26 20 corresponding straight-line solutions Y₁ (t) = (21(1))) and (t). nsider…

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: Solve using Power Series Centred Around Zero. Xy" + (1-x) y' + 2y=0 2=REZ+

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