Set the limits of integration for finding the volume of the solid inside the sphere x2 + y2 + z2 = 16 and outside the cylinder x2 + y2 =4. Sketch the region in 3-D and its corresponding region in 2-D

Q: Suppose A is a 5 x 5 matrix for which det(A) = -3. What is the value of det(2A)? det(2A) =

A: Sol:- Given :- Det(A) = -3 and Dimension of 5 * 5 Matrix

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A: Consider the initial value problem y'+43y=1-14t, y0=y0   To Find: The value of y0 for which the…

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Q: (c) Find an n such that P₂ is isomorphic to Rª. (Don't just state the value of n; prove why the…

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Q: 2. Let A be the matrix shown below A = [22] :) Find the matrix P that diagonalizes A.

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A: Given: The function, fx1,x2=x14+x23-2x12x22-10x1x22, the direction s=-1,2T and the point x=0,1T.…

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Q: Exercise 7.1.1 Find the equations and describe the shapes of the cross-sections when x = 0, y = 0…

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A: The given equation is: y4+2y''+y=9t+6 And the initial conditions are: y0=y'0=0, y''0=y30=1 We have…

Q: 4. y' (7x² - 1)/(7 + 5y) =

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Q: 25. Consider the problem a²uzz ut, 00 u(0,t) =0, uz(L,t)+yu(L,t) =0, t>0 u(x,0) =f(x), 0≤x≤L. (a)…

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Q: e the following constrained optimization problem using the method of Lagrange multipliers: max (x³ +…

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Q: Determine the infimum and supremum of the set S given by the grand union below. Write your answer as…

A: We want to find Supremum and Infimum of given set S.

Q: 2).  For an as follows, write the sum        an as a geometric series. a1 =  1 14 and  an an + 1

A: This is a question of infinite series.

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Q: (4) (a) Find the contour integral de using the Cauchy integral formula, where C is the positively…

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Q: 11. x²y" - 2xy + 2y = 0, y (1) = −1, y (2) = 1

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Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

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Q: Correct. If y, and y₂ are linearly independent solutions of ty" + 4y + tey = 0 and if W(y₁, y₂)(1) =…

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Q: (b) Let g(x, y) = 2 + 5x + 6xy + y². Find the degree 1 and degree 2 Taylor polynomials of g at…

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Q: ACTURE QUISION, IS DESCRIBED BY THE EQUATION y = COSH x WHERE X e Y ARE HORIZONTAL AND VERTICAL…

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Q: Question Solve: x-x+ 5y₁ = + 4" - 4y - 2x² = -2 with x (0) = y(0) = x² (0) = y² (0) = 0 Let & {√x…

A: Given x''-x+5y'=t                 (1)y''-4y-2x'=-2           (2) with x(0)=y(0)=x'(0)=y'(0)=0 Taking…

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Q: ) Find the Laurent series expansion of 1 (z − 1)(z- 3)² in ann(3, 0, 2).

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Q: 2. !. (n!)². > Show that there is no holomorphic function f (z) on any open set containing 0 such…

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Q: .] Let JE Mnn (C) be the following Jordan Matrix J = J3(-1) J5(-1) J7(-1) J₁ (2) J₂ (2) J₁ (2). a)…

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Q: The number of significant digits to which the number -1.26 approximates the number -1.244 is

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Q: Assume a function such that Y = (2x410)/(6x² + 5x). Obtain the first derivative. O f'(X) = (8x³ -…

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Q: The number of significant digits to which the number 7.29 approximates the number 7.01 is

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Q: I sin x cos x √sin x + 1

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Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

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Q: 25. Give the equation of each function whose graph is described below. a. The graph of y=x is…

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Q: 6. Let T: P₂ → P₂ be the linear operator defined as T (p(x)) = p(3x), and let B = {1, x,x²} be the…

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Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

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Q: (X- At which value does the function g(x)= 3x^4 - 4x^3 attain a the minimum value? Type answer as…

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Q: If a vector function v(t) = (t, ln t,t) is given for a scalar function Ø = x lnz+√√y − cos(x + 1)…

A: Given vector function is v(t)=t,lnt,t-2                    (1) scalar function is ϕ=xlnz+y-cosx+1,…

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Q: If csc(a) Give exact answers. sin (2) $ (-²/2) = COS an ( ½/7 ) = tan (in Quadrant 2), find

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Q: Use Trapezoidal Rule to find the lower bound m and the upper bound M of the value of the integral…

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Q: Find an integrating factor and solve the given equation. (12x + 3) + (4²+¹2) = 0 12y dy dx

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Q: For each of the following angles, convert to the other angle measure. 4π 3 Write answers exactly…

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