Example 7 Sketch the curves (a) r 1 (b) @ = 4. %3D in polar coordinates.

Q: e the inverse Laplace transform of

A: The given function is ss2+2s+2  to find the inverse Laplace Transform proceed as follows rewrite the…

Q: Q5) Find volume of body bounded by z = x - y from below and z = x + y from Above inside y = x² ,y =…

A: Volume bounded by the region

Q: dy dv S.S; as sin ny dedy Cii)

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Q: Use polar coordinates to evaluate sin (a² + y²)* dA, R where R is the region enclosed by the curves…

A: Here if we put limits in order dr dθ, then the given integral can not b evaluated so we need to put…

Q: TAKE THE ABSOLUTE VALUE OF YOUR ANSWER! torven: - 2T -T 271 a ftt)= Cos nt Fourier Series si か。…

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Q: 1. Consider A = (0, 4, 2) , B =, (6, –1,0) and C = (3,0, 1). (a) Find the unit vector having the…

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Q: Q5) Find volume of body bounded by z = x – y from below and z = x + y from Above inside y = x2 ,y =…

A: Volume bounded by the region

Q: nth If FCx): Ipn+ Rn, where In is the restita Taylor PolynomiaI and Rn ĥs the remainder, what must…

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Q: • Determine and draw the graph of the following equation in R3 : x2 + 212 + 2 8x + 12y – 2z + 35 = 0…

A: This is a problem of multi variable calculus, 3D geometry.

Q: too (4 – x)" /n + 5 9n · 7" Consider the power series n=1 Use Limit Comparison Test to show that the…

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Q: Given the matrix G -K and de = Then do and d, are G - conjugate if d, is given by Non of these

A: We know that,  Two vectors u, v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0  (Here…

Q: The student should answer the question below: The task is to find all relative extremum points and…

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Q: Convert dzdydx Into an integral of spherical coordinates (6coso p²sinodpdøde psinødpdøde Option 1…

A: We can solve this using spherical coordinates x = p sin(phi) cos(θ) y = p sin(phi) sin(θ) z= pcosϕ

Q: EVALUATE THE LAPLACE TRANSFORM OF THE GIVEN FUNCTION USING APPROPRIATE THEOREMS. 1. f(t) = et+1 cos…

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Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

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Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: Question 2, Let x(t) be a differentiable function defined on (-1,0) satisfying the following…

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Q: Consider the power series below: Show that series converges when x=11 (use alternating series test)

A: The given power series is                                                ∑n=1∞(4-x)n·n+59n·7n.…

Q: Consider an tan -1n • Determine if the sequence {an}=1 converges or diverges. n=] • Is the series an…

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Q: Consider the following: 1 2n an (tan-1 n) 1. Determine if the following sequence, {an}n=1, diverges…

A: Given : The given sequence  ann=1∞  is,  an = 21ntan-1n To prove : (1) To check whether the given…

Q: Determine if it converges or diverges

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Q: 00 (4-x)"· /n+5 9n · 7" n=1

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Q: Consider the differential equation xy - (1+ 3x)y + 3y = 0 If we know that the solution for this…

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Q: +00 For all x E R, eª = > ) n! n=0 Express f(x) = x²e* as a power series. • Find the third degree…

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Q: In solving one real root of tan x = 4x, what will be the appropriate iterative formula for the…

A: Given equation is tan(x) = 4x

Q: | In (a²) da -1 |

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Q: Consider the power series > 22n (2x – 1)". Vn2 +1 n=1 Use alternating series test to show that the…

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Q: A couple needs $50,000 as a down payment for a home. If they invest the $35,000 they have at 4%…

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Q: 2-X Evaluate the integral . S* dy dx using polar coordinate 0,

A: In polar coordinates  x=r cos θy=r sin θdxdy=r dr dθ

Q: Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic…

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Q: 2. Use integration by parts to evaluate the following. (a) Sx tan-1 x dx

A: Given integral is ∫xtan-1 x dx

Q: 10. Find a sequence of elementary matrices that can be used to write the matrix in rov echelon form…

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Q: if x<1: if 1<x < 4: 2x if 4<x.

A: Given the function is continuous therefore the left hand limit will be equal to right hand limit…

Q: 1. Let C be the curve with parametric equations V2 - t? 3/2 8 1 Y = t + 3 where t e [0,+). V2 8 (a)…

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Q: (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to…

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Q: Evaluate LL 4yzdsydydz O 15 O 15/2 O 10 O None of the choices

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Q: 1 III. Consider an 1 for n eN = {1, 2, 3, ...}. 2n + 1 2n + 3 Find a general formula for the kth…

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Q: 4. Find the exact length of the curve. Show All Work and Give Answer In Simplest Form. 2. r = cos´…

A: Arc length of the polar curve

Q: Find the areas for the following Vegions: Region boundad by 9 , and 3.

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Q: -2n2n 2n n 2) п En=1 1 —

A: Given series is ∑n=1∞1-2n2nn2n

Q: Use the 3rd degree Maclaurin polynomial for g(x) = r cos Write your answer in decimal form. to…

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Q: Please Show a FULL and DETAILED solution. Thank you so much for your help. • For all x E R, e* s+∞…

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Q: Q5) Find volume of body bounded by z = x – y from below and z = x +y from Above inside y = x² ,y =…

A: Volume bounded by the region

Q: The cost in dollars for removing p percent of pollutants from a river in Smith County is 72700p C(p)…

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Q: For all x E R, e* = Ln=0 +0+ n! Express f (x) = x e* as a power series.

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Q: n (4-x)"· / n+5 9n · 7" n=1

A: Given series is ∑n=1∞(4-x)n·n+59n·7n

Q: Determine whether the following series is conve rgent or divergent. (1.) (use Integral Test.) (2.)…

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Q: Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be…

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Q: Given: a, = In(n + 1) – In(n) for n E N %3D - {an}n=1 1.

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