1. y' - 4y = 0, y(0) = 1 2. y' + 4xy = e- 2x², y(0) = 0

Q: Suppose f(x) is a function with a critical point at x = 1. The graph of the second derivative of f…

A: Given, f(x) is a function with a critical point at x = 1.     Introduction: If x = a is a critical…

Q: Given the three vectors A = - 4x²y a -5xy²z a + 3x²z² a X B=2yz²a - 4xyz²a-xz² a X C=-3x³z a + xz a…

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Q: Given the vectors A=2a + 5a +7a₂ X y B=-a +6a +3a_ y 2 Evaluate the following Ba-3A O-2.5021a…

A: Given: The given vectors are:                        A→=2ax+5ay+7az…

Q: Solve the given initial-value problem. dx dt dy dt x(1) = 0, y(1) = 1 -5(t-1) x(t) = y(t) = = e =…

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Q: Let C₁ be a curve defined by the vector function R(t) = √2 costi+ sint j + sint k a) Find the moving…

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Q: 4. Evaluate the given definite integral 0 fa₁- - 2x) dx -2

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Q: Determine the scalar projection of A=3a2a - 4a y Z in the direction of B=a +5a - 6a_ y X N

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Q: 7. Find a power series representation for the function and determine the interval of convergence. X…

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Q: Surface area using an explicit description Find the area ofthe following surfaces using an explicit…

A: The paraboloid z=2x2+y2, for 0≤z≤8. We have to find the area of the given surface.

Q: ←6 FP 3 L I √²³ Sªp² sin(ø)dpdfød 0 ㅠ

A: Given: 0≤ρ≤3 , 0≤θ≤π2 , 0≤ϕ≤π6 To sketch region  To find : Volume of Solid  V=∫0π6∫0π2∫03 ρ2 sinϕ dρ…

Q: f(x) = √√x

A: To approximate the function f(x) up to degree 2 and estimate the error.

Q: 40, 41, 42, and 43 Find the radius of convergence and interval of convergence of the series. 40(-1)"…

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Q: 1. The perimeter p f a square varies directly as its side. A square of side 1.0 cm has a perimeter…

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Q: 10. Compute the area of the region bounded by circles x² + y² = 2x and x² + y² = 2y.

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Q: Determine the values of a where the function f (x) is not continuous. Label each discontinuity as…

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Q: 1 / / / / 1^^ 1 / // | \₁ 1/ // ||^~ /////|55 // / //\ Euler's Method / / / / / AS |/ // // | \\…

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Q: How would I prove that for any sets N, M there is an equivalence N x M~M x

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Q: NO CALCULATOR IS ALLOWED FOR THIS QUESTION Show all of your work, even though the question may not…

A: Position function given by st=t2tan1t for t>1 To find velocity we can use derivative

Q: 16. A triangle has vertices at points in the Argand diagram which represent the complex numbers z₁,…

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Q: Question 1 Find a bound for the number of bisection method iterations needed to achieve an…

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Q: Let F = (7z+7x4) 7 + (3y + 2z + 2 sin(14)) 7 + (7x + 2y + 3e²¹ ) k. (a) Find curl F. curl F = (b)…

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Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

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Q: 10) Consider the following linear programming problem Max                         8X + 7Y s.t.…

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Q: Work integrals Given the force field F, find the work required to move an object on the given…

A: Given force field is:F=x, y, zx2+y2+z2. We have to find the work required to move an object on the…

Q: 14. Apply Green's Theorem to evaluate the following integral: f (1 − y³)dx + (x³ + e¹²³) dy where is…

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Q: Let V = R4 equipped with the dot product. Let S = Span (GG) a. Compute projs (ū). b. Compute perps…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: The following is a time series for the last 6 months of 2016 50        54          65       58…

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Q: Finding potential functions Determine whether the following vector fields are conservative on the…

A: The given vector field, F=y+z, x+z, x+y on ℝ3. We have to check whether the vector field is…

Q: Utilize the fourth order Taylor polynomial for e7x at x=0 in order to approximate the value of e1.2…

A: The fourth order of the Taylor Polynomial T4(f; c)(x) to function f(x), based at x=c, is:…

Q: Practice Identify y-int, x-intis), axis of symmetry, vertex from the following equations. Then graph…

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Q: a) Find the characteristic polynomial, the real eigenvalues, and the corresponding -1 0 0…

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Q: x' = y y' = x" + 6- -5y- X 1 + x² - 6x 2 1+x² + 5x' = 0 Find all critical points of the resulting…

A: Given:        x'=y          and y'=-5y-6x1+x2 To Find: We have to find the critical points of the…

Q: Let f and g be bijections such that fog is defined. Prove that fog is bijective.

A: Introduction: If a function f: A→B meets both the injective (one-to-one function) and surjective…

Q: 12. Is this statement valid? If gas prices go up, more people will commute. The number of commuters…

A: If the gas prices go up, more people will commute.  The number of commuters went up, therefore gas…

Q: Construct a matrix whose column space contains (1, 1, 5) and (0, 3, 1) and whose nullspace contains…

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Q: Definition 1. Let X and Y be two topological spaces. A map f: XY is proper if the preimage under f…

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Q: Exercise 17.3.11. Let f: {-3,-2,-1,0, 1,2,3} → Z be defined by f(x) = x². (a) What is the range of…

A: Please check step 2 for solution.!

Q: Use the ratio test to determine whether an+1 lim n→∞ an n=16 (a) Find the ratio of successive terms.…

A: First we calculate the ratio then find the limit. According to D' Almbert ratio test series is…

Q: Solve the given system of differential equations by systematic elimination.

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Q: Given the three vectors A=-2xyz²a +3za - 2 az y B=4y²₂² a 2xz a – 6yz a - y z Ĉ=x²²a_+2yz²a₁ - 4x²y…

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Q: y"" 1 x² ln x

A: As per our guideline, we are supposed to solve only one question. Kindly repost other question as…

Q: Consider the series (-1)+112n-1 n=1 (n+5)3 11+2 In this problem you must attempt to use the Ratio…

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Q: If two rotation quaternions are p = [0.866, 0.162, 0.382, 0.279] and q = [0.924, 0.207, 0.110,…

A: The multiplication of two quaternions p→=p0+p1i⇀+p2j⇀+p3k⇀ and q→=q0+q1i⇀+q2j⇀+q3k⇀ is given by…

Q: Find the optimum of f(x) = 2.2x-1.7x² + x³ -0.25x Perform: (Round-off all computed values to 4…

A: We know the golden ratio is 0.618.  We need to find the value of d where d = 0.618b-a For our first…

Q: The given figure illustrates the graph of the set of feasible points of a linear programming…

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Q: We have measured value A = 81.8 ± 5.6 and value B = 35.8 ± 7. Find the largest and smallest possible…

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Q: Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105…

A: Given: Two tanks are partially filled with 100 gallons of brine. 105 pounds and 45 pounds of salt…

Q: 1 given function, F(t) = AF (H) 1 M. 3 لا -3 3 04+2 3 3 -3 -3 <+ ²0 9 15 vt

A: By Complex Fourier series:

Q: Use the ratio test to determine whether n8n n=22 (+2)! (a) Find the ratio of successive terms. Write…

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Q: a. Compute y' in terms of a, z and y. b. There are two points on the curve where y' = 0. One is at…

A: As per the company rule, we are supposed to solve the first three sub-parts of a problem. Therefore…