Use the binomial series to find the Maclaurin series for the function. 1 f(x) = 3 (1+x) f(x) E n=0 = X

Q: ди 10²u = It 40x²¹ together with the boundary conditions u(0, t) = 0 and u(, t) = 0 for t≥0 and the…

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Q: (a) Define Fourier series. The function x is periodic with period 21 on the interval [1,-1]. Find…

A: Fourier series: Fourier series of function fx on the interval -L≤x≤L is defined as   where,…

Q: solve the differential equation x2yy'=(y2-1)3/2

A: To solve the given differential equation :-

Q: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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Q: Q4: Find the dual graph of G G

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Q: Explain why the two planes P, 7=(2,5,3)+(2,-1,-3) +/(1,0,-1), s,/ € R, and P',:…

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Q: 4. Find the inverse Laplace transform of 1/(s² + 4s + 5) Enter your answer

A: Solution :   Given that  1s2+4s+5

Q: For the following problems, use the method of shells to approximate the volumes of some common…

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Q: Find the roots of complex numbers √√64 e¹.4i if n=4, k= 0,1,2,3 k=0, z1= k=1,z2= k=2, z3= k=3, z4=

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Q: Using the I) Method of Successive Substitution, the II) Bisection Method, and the III) Regula-Falsi…

A: Given the function 3x=ex-sinx Find the root of the function in the interval 0,1 using Bisection…

Q: Consider the function with the graph shown below. f(t) 4 Select the option that best describes this…

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Q: Here a calculus question about continuity. I'm unsure about my answers. Please explain

A: We use definition and properties of Riemann integral.

Q: (a) Write down and OB in terms of the unit vectors i, j and k. (b) Calculate OA OB and hence…

A: Solution:a) Taking O as origin OA→= i^+k^OB→=j^+k^b)OA→.OB→=(i^+k^).(j^+k^)=1Also, |OA→|=2,…

Q: Determine the total weight of the minimum Hamilton circuits?

A: Given

Q: Consider the partition P of [0, 1] be given by P = {0, 1/8, 1/4, 1/3, 2/3, 3/4, 1}. What is the norm…

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Q: ASAP

A: We solve by using Laplace Transform.

Q: f16 sin²x cos²x dx

A: Sol

Q: fin (x In (x + x²) dx

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Q: EXAMPLE 2 Consider again our analysis of a heavy rock blown straight up from the ground by a…

A: according to question, velocity of the rock at any time t during its motion is given by  vt=160-32t…

Q: H.W. Solve the D.E. (using Laplace, trans.) 3+4y=2sinet given that y (0)=0, 9(0)=d

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Q: Q1 Rewrite the polar equation r= 2sin0cose in Cartesian form- Q2 Convert the Cartesian equation to…

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Q: Write the following expression using one exponent: (25-35)7. Show process.

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Q: Q3 Find the area of the region that bounded by r=1- cos(0)

A: We have to find the area of the given cardiod.

Q: Use the graph of f(x) = √x to write an equation for the function represented by each graph. (a) g(x)…

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Q: Convert the numeral to a numeral in base 10. 24516 24516 = 10

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Q: The surfaces r = 2 and 4,0 = 30° and 50°, and p = 20° and 60° identify a closed surface. (a) Find…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: uxx + uyy =0, 0<x<a, 0 <y<b, B.C. u(x, 0) = 0, u(x, b) = f(x), 0 ≤ x ≤ a, ux(0, y) = 0, ux(a, y) =0,…

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Q: Find an orthonormal basis [b1,b₂, b3] of spom[3] Lohere B={(1,0,1), (1, 0,-1), (0₂1, 2)}, using the…

A: We Know that,  Gram–Schmidt process is a method for orthonormalizing a set of vectors in an inner…

Q: A dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.  How many sets of 7…

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Q: divisible by 3

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Q: 1. Use the definition to find the first five nonzero terms of the Taylor polynomial, centered at c =…

A: To find the Taylor polynomial of function f(x) =1/x centered at c=1

Q: B. Solve the Initial Value Problem(IVP) for the following Nonlinear ODE (Bernoulli equation) y' + xy…

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Q: Q3 Find the area inside one leaf of the three leaved rose r-cos30 (upper lim and lower limit= n/6)

A: Given: The value of r and the value of θ. To find: Area inside of 1 loop. As per policy guidelines,…

Q: A 5 2 9 4 6 B 2 8 5 7 D 3 C

A: The given graph is

Q: Given f(x) = 9+8x² + x¹, find the following: a. The galois group of f(x). b. The subfields of…

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Q: Sdz dx dy=1 dz dy dx=24

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Q: 42. Which of the following graphs contains a cut-vertex? A. Complete graph K3 B. cycle C4 C. path P2…

A: Sol

Q: 18. How many edges has each of the path graph P158? A. 155 B. 156 C. 157 D. 158

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Q: The parametric equations of a curve is x = = 3 sint, y = 3 cost and z = 4. (a) Sketch the curve r(t)…

A: The given parametric curve is x=3sint, y=3cost, z=4. (a).  To draw the given curve rt=3sint, 3cost,…

Q: f(z) = z²e¨²?

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Q: Find the solution of the given initial value problem in explicit form. Determine the interval in…

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Q: o Vector - U+ U Note: In both graphs, each box is 1 unit by 1 unit in size

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Q: Evaluate the Inverse Laplace transformation of the following functions

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Q: Can this graph be traced? Use Euler’s theorem.

A: Euler's theorem says that a connected graph has an Euler cycle if and only if every vertex has even…

Q: GET THE EQUATION ㅇ 20 OF THE GRAPH 00 49 ① LUNAND t

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Q: Q 1 Find all points in the first quadrant where r = 2sin(30) and r = 1 intersect. r=2sin(30) Q2 Find…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: Problem Solving 1. For the following problems, determine the area of the region between the two…

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Q: The perimeter of a rectangle is 190 meters. Express the area A as a function of the length L, and…

A: The solution is given as

Q: 2₁ = 2² - 3xe 4 and 2₂=-4x4-3e-4 are solutions of the nonhomogeneous y" + p(x)y' +q(r)y = f(x). 3₁…

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