a) Compute these two integrals shown below using one application of trapezoidal rule and Simpson's 1/3 rule. fxdx [x² cos(x) dx

Q: 2. Given that 9+² -3 (-1)n+1 = n=0 32n+1 X². Obtain the power series representation of each o…

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Q: F C

A: FEBAEFD is  a path  FBCCD is a path FEABFD is a path

Q: 2. An oven technician charges a call-out fee of $50 and an additional $20 per hour for the duration…

A: The call out fee is $50 additional fee per hour = $20 per hour let t be the number of hours…

Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

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Q: The points P(-1,0, 4), Q(1, 2, 4) and (0, -1, 3) are vertices of a right triangle.

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Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: x=ρsinϕcosθ y=ρsinϕsinθ z=ρcosϕ For the cone: z=√(3(x2+y2)) or ρcosφ=√3sinφ=> tanφ=1/√3 or φ=π/6.…

Q: 3.4.4 By transforming to polar coordinates, show that the double integral (x² + y²) ² dx dy (xy)²…

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Q: Which of the following functions are of exponential order? (a) t³ sint (b) 100e49 (c) e¹³

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Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

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Q: = 72. P(₁,1) and P(r2, 82) represent the same point in polar coordinates, then ri

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Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

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Q: can you elaborate the solution for letter a ? please

A: The surface is two - sheeted hyperboloid. The graph of surface is given below.

Q: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on a…

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Q: Taylor series of the following ) = ln(1+x), a = 0. ) = x² + 2, a = −1.

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Q: Write down the first three terms of the Taylor series expansions of the functions dx (t-h) and dx dt…

A: Problem is solved using concept of taylor series theorem.  Thaylor's theorem states that:

Q: Thermic effect of food above RMR (kJ.h-¹) 80 60 20 h 5-- 5 x h kJ 0 0 1 2 3 5 6 Time (h) Figure 3.…

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Q: Q4) Consider the function f(x)= x³ -7x+3=0. Use Newton Method, find the positive root of…

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Q: Find the curl of position vector O Find divergence of A, where A = 2x²z i -2y³z²j +4 y²z k

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Q: (B) let y = 3sin5x2cos5x show that y + 25y = 0

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Q: (b) Determine a cycle decomposition of a hypercube Q4-

A: Here, we need to determine a cycle decomposition of a hypercube Q4

Q: Hand written plz Consider the full and reduced singular value decompositions (SVD) of a square…

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Q: 2 1. Given a space curve a:1= [0,2m] → R³, such that a ()= a(), then a(t) is... Curve A. a closed D.…

A: Solution : 1  Option ( B) is correct  Simple

Q: Find the line integral F.dr of the vector field F=ax] over a curve C defined by a C rectangle in the…

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Q: 5. In how many ways can 7 boys be seated in a circular order?

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Q: {1,2,...,8) and zy e Eit and only if my Va Oa. n 8, m 8,r 2 Ob. n 16, m Oc. none of the choices Od.…

A: Given : set of vertices V=1, 2, . . . . , 8 and xy∈E if and only if x, y∈V, x≠y, x-y is odd The…

Q: Use the second-order predictor-corrector method (that is, the first-order Adams-Bashforth formula as…

A: Answer is given using second-order predictor-corrector method.

Q: f(s) = s² +5 2 3s³+2s²+5s find f(t)

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Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

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Q: 7. Set-up the triple integral for the volume of the solid S enclosed by the paraboloid z = 4 + x² +…

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Q: Find the formula for the number of ways for putting n identical balls into k distinct boxes so that…

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Q: Let p,q and r be the propositions p: Grizzly bears have been seen in the area. q: Hiking is safe on…

A: We know that ,  A proposition is a Mathematical Statement which is either True or False. Also , we…

Q: f(x) = x³, y = 1, x = 1 Find the volume of the solid obtained by rotating the region A about the…

A: Solution :

Q: Sketch the domain of integration of the double integral (√(1-x²) La d.x dy x+y √(x² + y²) 0 0 and…

A: We will find boundary curve for domain of integration  . To find value of integral we will use polar…

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: Region B is bounded by the Red Colour graph.

Q: (III) Find the Half-range Sine series of f(x) = sin(x) on (0,2).

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Q: If Q, R, S are sets then QU(ROS) and (S-(QUR)) U (R- (QUS))) are disjoint sets.

A: This is a problem of the set theory.

Q: dx 3. Evaluate the integral I = S₁ x² + 6x +10 Include 4 decimal places on your computation. a.…

A: Given  I=∫01 dxx2+6x+10 Here a=0, b=0 anf f(x)=1x2+6x+10

Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…

A: here, We have to derive the heat equation with a metal rod with variable cross-sectional area A(x).…

Q: The two directed graphs below are isomorphic. Select one: True False

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Q: Find the general solution to the differential equation (7x+5y)dx + (5x - 8y³)dy = 0

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Q: (a) How many positive integers divide 10!.

A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

Q: Find the Fourier series for the periodic function giving below -1, -π < t < -π/2 x(t) 0, -π/2 < t <…

A: Fourier series of the given periodic function

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: b) Solve the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy=0.

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Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x- 2ky + 5z = 0…

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Given  R=0≤x≤1, 0≤y≤1-x2,0≤z≤4-x2+y2 The region is  The region in XY plane

Q: 1. Write each of the following in "If p, then q" form. a. Every square is a rectangle. b. Being…

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

Q: 3 2 Y 4 -2 -2.69, -1.33) -2 a. The terminal point is how many radius lenghts to the right of the…

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Q: For the function i. ii. iii. Z Z 1 1 (1+z)(3+z)_2\1+z_3+z, the region |z| 3. find the Laurent series…

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