67 V3 1 Use De Moivre's Theorem to express the complex number on the form a+ bi. ---1

Q: in Exercises 22-26 solve the initial value problem. 22. y"-7y + 6y = -e*(17 cos x -7 sinx). y(0) =…

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Q: Determine whether the improper integral (3- is convergent or divergent.

A: The given integral,       ∫1∞3-2x-32dx

Q: 2. Determine x >0 for each case: 5903 = x (mod 60), 17342 =r (mod 5).

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1) Vw(19, 5, -1) =

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Q: 12. f(a) = 2x" -x -3 12. f(x)- x+1 1-1 if x50 13. f(x)3= %D 4x if x>0 14. f(x)= x-1

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Q: 4. Solve the matrix equation for x and y. 2 1 5 3 -2 -2 1 x 9 5 у %3D 1 -3

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Q: I (z sin(x) + y² )dV Evaluate 5 5 B = {(x, Y, 2)|– as *<I<,4 < y< 8,4 < z < 6} . %3D 6. Round your…

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Q: Determine

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Q: I need help with "Determine whether the lines L_1 and L_2 are parallel, skew, or intersecting. If…

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Q: 3 -5 6. Evaluate the determinant for the following matrix: 1 O A. 8 О В. -2 О С. 5 O D. -4

A: Solving the problem by finding the value of the determinant.

Q: Determine whether the improper integral 3-2x) /2 dr onvergent or divergent.

A: We have to find the integral

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: Find the gradient of the function at the given point. f(x, y) = 3x + 4y2 + 10, (3, 4) ∇f(3, 4) =

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: x°e3» dx (Repeated Integration by Parts)

A: Find your answer below

Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: Determine whether each improper integral below converges or diverges. dx 3. S 0 x* + 2x – 3

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Q: (5x) сos (Зa')dx COS

A: LetI=∫cos5xcos3xdxI=12∫2cos5xcos3xdxWe know…

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (11, 10, −7) ∇w(11, 10,…

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Q: C Solve the following problems. 16. What value of k makes the function continuous at x= 3? Graph the…

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Q: 2 sinh x 2. Calculate the integral, dx. 5+6 cosh x

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Q: F. Boolean Matrices Го 1 A = 1 0 3-- [1 0 1] C=0 1 1 0 1 0 [1 1 1] D= 0 0 1 |1 0 0 Let B = [1 0 0 1]…

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Q: Evaluate the iterates integrals r*dA D = {(r, y) : 1<r< e, 0< y S In(x)} %3D

A: We will use simple Integration rules to solve this question.

Q: Applications of Integral calculus 3. The following curves bounds a certain area: y = 4x – x2

A: Area bounded by a curve y=f(x) on [a,b] is given by, A= ∫abydx

Q: Solve the differential equation with appropriate method. Finalize answer equated to y. y' = 2xy - x

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Q: b. f(x) = x - 3 x² – 9 2-

A: The given function is,   f(x)=x-3x2-9

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: A closed rectangular box with a volume of 375ft° is made from two kinds of materials. The top and…

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Q: C/4 41. (x³ + x* tan x) dx 7/4

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Q: What does the notation AV12, 2.5) mean? It is the instantaneous velocity O It is the average value…

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Q: S(In x)³ dx

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Q: val [1,5].

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Q: Consider the points A(3, –3, 3), B(4, –5, 1), C(-2, -4, 1), and D(6,3, –5). |(a) Find the volume of…

A: Let's find.

Q: 1 The series > is convergent. (Зп + 1)(3п + 4) n=1

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Q: 7 dx 5. S- xVx-4

A: I am attaching image so that you understand each and every step.

Q: Find the total area of the shaded regions. y=x√(36+x^2)

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Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

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Q: 2. Find the directions cosines of AB. a. Ā = (-1,2,3) and B = (4, –3, 1) %3D

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Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = 2 ¿i + k - Duf i

A: Given that       f(x,y,z) = 6x5y3z4 ; P(1,-2,1); u=(1/3)I+(2/3)j-(2/3)k  Here we have to find Duf at…

Q: 1 dx x2 V25 – x2

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 27. x(2 + x') dx Jo

A: integration

Q: Suppose that it is given to you that f′(x)=(x+5)(10−x)(15−x) 1.The first inflection point (from the…

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Q: State whether each of the following series converges absolutely, conditionally, or not at all. n²…

A: A series ∑an is called absolutely convergent if ∑ an is convergent . Limit Comparison Test :   If…

Q: 43, 44, and 45 Evaluate the integral by changing to spherical coordinates. 43. xy dz dy dr

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Q: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

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Q: 5. Evaluate the indefinite integral, ſ' coth- dx. - 6.

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Q: Suppose that o f(x) dx = 3. Find , f(x) dx if, %3D

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Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

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Q: panding such that its length is always 4 times its width. If the ng at a rate of 0.5 cm/min, is its…

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