5. Evaluate the following integrals: (a) *³ ** cos(x) dx dy 4y -x²-y² (b) √ √ ² dy dx (Hint: Use polar coordinates)

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A: Solution

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Q: 5. Solve y" - 3y + 2y = 2et, y(0) = 2, y'(0) = -1 a. et + 4et-e²t b. et + 4e²e²t - et + 4et-e²t d.…

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Q: 32. Evaluate: lim X18 10 (x + 1)¹⁰ + (x + 2)¹0 + 10 X + (x + 2012) ¹0 ... + 2012¹0

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Q: Formulate a 4th order interpolating polynomial that models the COVID cases in the Philippines from…

A: firstly we will take points for interpolation:- i     xi        y 0    4      72848 1    5…

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Q: The numerical value of 34 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: Example 2.33. Evaluate the following (correct to four decimal places) by Newton's iteration method :…

A: (i) To find: the value of 131. Please post the multiple questions separately. Here I answered 1st…

Q: The numerical value of S X -3 9-x² dx will be equal to *******

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Q: Example 4.16. Using House-holder's method, reduce the following matrix to the tri- 1 diagonal form:…

A: First check  about the symmetricity (A square matrix  A is called symmetric if A=AT) AT=143412321…

Q: Q1. The following table gives the values of an experiment at various sample z Zi 0.3 0.4 0.5 0.6 0.7…

A: Note that as per the company policy, we are allowed to solve only the first 3 sub-parts of this…

Q: Find the Laplace transform of the following: 1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: To find the Laplace transform of the problem.

Q: Let (G, 0) be a group and x € G. Suppose H is a subgroup of G that contains x. Which of the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find and classify all critical points of the function cs f(x, y) = x³ + 2y - In(x³y³)

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Q: Determine the value of k for which Assume that k is a positive number. k 4 k 2k | = 0

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Q: Example 2.20. Find the root of the equation cos x = xe* using the regula-falsi method correct to…

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Q: create 2 sample word problems of antidifferentiation with solutions

A: First problem: The rate of water out of a faucet is rt=t3, where t is the number of minutes from the…

Q: Example 2.22. Use the method of false position, to find the fourth root of 32 correct to three…

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Q: sin (xy) Which ONE of the following statements is TRUE with regards to lim (x,y) → (0,0) x² + y² A.…

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Q: y" — y' — 6y = t²e³t — 4t², y(0) = 0, y' (0) = -1

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Q: The curve has an equation of x = y^3, find the radius of gyration with respect to the x-axis. * 0.89…

A: Given curve is x=y3. We have to find the radius of gyration with respect to the x-axis. Since, no…

Q: The interval of convergence of the series Σ(√n+1-√n)(x+2)" is given by n=0 A. -3<x≤ - 1. B. -3<x<…

A: The given power series is                                 ∑n=0∞n+1-n(x+2)n

Q: Find the power series solution of y " – 2 xy ' + x2y = 0, with y(0) = 0, y '(0) = 1. Give the first…

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Q: 4. Let V be a vector space over R with subspaces U and W. (e) Show that 1 0 -1 1 and define LA: R4 →…

A: 4.c

Q: 1. If f(x) = x³ + x is a periodic function with period 2π, then the Fourier series will have the…

A: We have to find the correct options for the given equation.

Q: Given two Vectors U = [4 +2]. an .and V= Find U+12V Draw Vectors U and V and 10+ as arrows in a…

A: U=25 and V=82

Q: 4. Find the solution for the following y""+y"+ 2y = 3 y(0)= 1, y(0)=1,y)=1

A: Solution :-

Q: If R is the disc with center at the origin and radius 5 then the numerical value of Lxds R xdA is…

A: We have to find the numerical value of  ∫RxdAwhere R is the disc with centre at origin and radius 5.

Q: Which ONE of the following is NOT the critical point of the function f(x,y)=xye-(x² + y²)/2₂ A.…

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Q: v" - 4v" +5v' - 2y = 7t-5. v(0) = 0. v'(0) = 0. v"(0) = -2

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Q: II. Assume that A and B are False, and C, D, and E are True. What is the truth-value of the…

A: We will use the truth table to find the truth Values.

Q: 12. Touching all vertices in a graph without repeating or picking up your pencil and starting and…

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Q: Determine the value of k for which Assume that k is a positive number. k 4 2k k 1 = 0

A: Let us considre a 2 x 2 matrix A=abcd The determinant of the matrix is obtained as |A|=abcd=ad-bc A…

Q: Let f= (1 2) (364) and g = (1 4) (2 5 3) be permutations in S6, written in cycle notation. What is…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. The y - coordinate of the centroid of the…

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Q: t₁ g(t): (t-4)², (9t-e20-4t t<3 3<t<5 125

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Q: f(x) = sin (√x) - x

A: Solution : Fixed point iteration, f(x)=sin(x)-x Taking  a=-0.5b=0.5 f(a)&lt;0  and  f(b)&gt;0 Means…

Q: Which is the main connective of the following sentence: -(FG)→ H A. - B.. C. → D. O

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let S be the following relation on C\{0}: S = {(x, y) = (C\{0})² : y/x is real}. Prove that S is an…

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Q: 24. In order for a linear programming problem to have a unique solution, the solution must exist OA)…

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Q: b) Find the inverse Laplace transform of the following function: 3s +6 F(s) = s² +9s + 5.

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Q: 33. Evalaute: lim n→∞ •n + 2 (n − 1) +

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Q: Consider the region on the 1st quadrant bounded by y = √4x², x and y- axes. If the region is…

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Q: 2. In Michigan the rate of real estate transfer tax is $3.75 for each $500 or fraction thereof.…

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