6. Evaluate the following multiple integrals. π +2 (a) y sin(xy)dady (b) [1² fr esc² 0dødr π/4 π/2 © f f f ² 0 ze-y²dxdydz

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Q: (B) Use Tabular integration to evaluate the following: - f(t³ - 4t² + 5t + 32)sin(t)dt

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Q: a. Determine the Cartesian equation of the plane that has x-, y-, and z-intercepts at 2, -4, and 3…

A: Here we will find all equations,

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A: see below the answer with explanation

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Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

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Q: Question 1. (5 marks) Find the distance between the point A = (2,2,3) and the line L : x = -1-4t, y…

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Q: 3. What value of k will make the line with symmetric equations - (1,−1,3)+s(3,2,2) p vector equation…

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Q: n. 3' 11. In each of the following, express the required series in summation notation.' (b) Find the…

A: Let's find taylor series of given  function  f(x) = sin(2x) at x = pi/6.

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Q: Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+32)sin(t)dt

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Q: 7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes…

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Q: Find the derivative of the trigonometric function. y(x) = cos(sqrt(sin(cot(pi*x))))

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Q: Find the derivative of the function. <-2 g(x) = (7x² - - ² 4 4x + 7 g'(x) = 2 ((7x²-4) (28x²…

A: g(x)=7x2-44x+7-2 Chain rule: f(u(x))=f'(u(x))·u'(x)

Q: Find the equation of a circle whose center is at the intersection between the lines 3x - y = 2 and…

A: The standard form of the equation of a circle is x-h2+y-k2=r2 where (h, k) is the center of the…

Q: Find the derivative of each of the following functions:- log₂ x 2. y=- X

A: The given data is: y=log2(x)x   To find the derivative.

Q: Q2: (A) Show that if y=csc(u), then dy -csc(u) cot(u) du dx

A: I have stated the used formula in the solution

Q: 1. Find the volume of a solid if the area boun ded by the curve y = In x, the x-axis and the line x…

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Q: xy = 1, y = 0, x = 1, and x = 2 is rotated about the line x=-1.

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Q: Evaluate the following: 1. [ sinh(4)dæ

A: Application of integration

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Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Solve the given by simple substitution (2x + y)² dx - 2dy = 0

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Q: 1. [(5x (5x - 3)100 dx 2. [(x − 3)¹/4 da dx 5 3. · / ( 2² + ² ) ( ²2 2²³ + 2) * dx 2 3

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Q: Find the solution of the given initial value problem. ty' + 2y = sint, y() = 9, t>0 y

A: y' +2t y =sin ttEquation is of Bernouli's form:P(t)=2tIntegrating Factor:I.F.=e∫ P(t) dt     =e∫2t…

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Q: . Determine if AABC is a right-angled triangle, given A(1, 6, −2), B(2, 5, 3), and C(5, 3, 2).

A: Find the squares of all the sides of the triangle and then observe them

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A: answer is in next step

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Q: Next question -4b3 {b₁,b2,b3} be bases for a vector space V, and suppose a₁ = 6b₁ b₂, a₂ = − b₁ +…

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Q: Q1: If the function f(x) define as f: R →R such that f(x)= (x+1, x>2 x²-1, x≤2 Show that the…

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Q: Figure out the generated volume of rotation the region surrounded by = 4x² and y=4x about X-axis.

A: find intersection point

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A: Given, Annual rent=$950,000, interest rate=8%=0.08

Q: Question 7 (a) Find if x² + y² + xy = 1 dy dx (b) Identify the nature of the stationary points of…

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Q: Find the equation of the plane that passes through the points (3, -2, 2), (-9, 2, 4) and (-6, -4,…

A: We need to find equation of plane.

Q: (3x²-3x-4) 2x²-3

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Q: C. Find the volume of the solid generated by revolving the area bounded by the given curves about…

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Q: Tutorial Exercise Calculate two iterations of Newton's Method to approximate a zero of the function…

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Q: 7. fx√x - 1dx 8. 9. √ (2) √2² - 1 da dx 1 15. dx 5x + 1

A: 7. ∫ xx-1dx

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Q: B. Find the area bounded by the given curves Show the graph (you can use any graphing software,…

A: A detailed solution is given below.

Q: Q 19 If a fault cuts three sides of a quadrilateral, then: Red with one of the vertices 2- Cut the…

A: Given question:- 19) if a fault cuts three sides of a quadrilateral then,

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