Show that sin(x)  can be approximated by x-x3/6  within 0.01 on the interval [-1,1].

Q: 3. Find the Maclaurin series for ƒ(x) = ln(1+x) using the definition of a Maclaurin series. Also,…

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Q: Q2) Determine using Cauchy Riemann equations the function below is analytic or not? 2z4-8z5+4z6…

A: If f(z)=u(x,y)+iv(x,y) then Cauchy-Riemann Equations is ∂u/∂x=∂v/∂y and ∂u/∂y=−∂v/∂x

Q: (a) Define a metric space (X, p). (b) Let p: R+ → R+ be a function defined by ln (2). Prove that p…

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Q: 3. a) Is there exists a linear map T: R2 R2 for which T(7,7)=(4,-5) and T(2,2)=(8,-2)? Justify your…

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Q: 5.(- Let the surface S be the graph of the function z = g(x, y) = x + y over the unit disk D:+y² ≤1.…

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Q: Problem 15. Determine which of the following sets are subspaces of R³ ? V 1.4r, 52,-27 z arbitrary…

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Q: If S1, S2, & S3 have respective ratios of 5, 3, & 7, the leaving variable using the "Simplex Method"…

A: According to guidelines here i am solving first questions only.kindly post another question…

Q: A car drived 50 km on a bearing of 125°. If its position is defined in terms of Cartesian…

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Q: Exercise 12. Let B = {(0,1,0), (1,-1,1), (1,1,2)} be a basis for R³. Applying Gram- Schmidt process…

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Q: Given the following first-order ODE: dy dt =y+t³ , where t is evaluated from t = 0 to t= 1.5 with…

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Q: Compute the following integrals using Residue Theorem. 52 - 2 a. b. dz 232-27 4² dz Soz (z − 2)4 dz,…

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Q: Convert f(t) in terms of step functions and find the Laplace transform using appropriate property. S…

A: Solution

Q: Subject

A: We use line integral to solve given integral.

Q: One of the following statements is true:

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Q: Solve the Bessel differential equation given below for y(1.5) under the boundary conditions given by…

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Q: enough protein and iron to meet at least the DOH recommended daily allowance (RDA) for each…

A: The linear program using the Simplex method as,

Q: 2. The Dual model a. Is derived systematically from the Primal model b. provides the decision maker…

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Q: in fuzzy graph

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Q: III. Consider the parabola C: 2-4 = -(x - 2)² on the xz-plane. 1. Find the center-radius form of the…

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Q: Homework: Determined whether the following sets are open or closed in (R¹, 1) [a,b] x x [an, bn];…

A: As per our company guideline we are supposed to answer only one question with its 3 subparts.  So I…

Q: Discuss the difference between harmonic and conjugate harmonic function. Also find the analytic…

A: The given problem is to discuss the difference between harmonic and conjugate harmonic function and…

Q: A customer purchase $28.14 in products only $12.83 is taxable. How much sales tax is owed if the tax…

A: Given that a customer purchase $28.14 in products only $12.83 is taxable. Also given that the tax…

Q: 2. Using laplace transforms solve for x and y: dx dy + dt dt 2dx dy + + x +y = 3 dt dt subject to…

A: The solution is given as

Q: xº. Prove that the function f(x)=2 a concave function. For this purpose, compute the Hessian matrix…

A: Here given function is a single variable function so we can use double derivative test to check the…

Q: 3.0 Let T: R³ R be a temperature function defined as T(x, y, z) = x² - y² + 2xyz. Find the heat flux…

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Q: True or False? 6. Let x and y be real numbers. We have that |x| = |y| if and only if x = y.

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Q: 1. Use the Cauchy-Riemann conditions to find out whether the following functions are analytic. a.…

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Q: Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s…

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Q: Two forces are acting on a point. The first force has a horizontal component of 5 newtons and a…

A: The complex number z=x+iy can be plotted in the complex plane by moving x units along the real axis…

Q: Find the volume of the solid generated by revolving the area bounded by x² − 2kx − 3ky + k² = 0 and…

A: Please see the attachment

Q: Q.1A) In application of partial equation show: If Z-f(x,y) & the values of x-(u²-²) &y-u.v: then…

A: Solution

Q: Let y(t) denote the solution of the given initial value problem. Is it possible for the…

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Q: x sinx find dy for y dx √(x-1) (x²+1) Evaluate f(u² + 2u + 3)² (u + 1)du

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Q: dz Z 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using direct…

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Q: Consider

A: We find the general solution by finding roots of equation.

Q: Solve for z in the equation 2-5j z+j+1 2= +3j 2z-j A) 0.2 + 0.1 j B) -0.2 + 0.1 j C) 0.2-0.1j D)…

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Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

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Q: Compute the value of the constant k for which kx²e5x is a particular solution of the differential…

A: We compute the value of the constant k for which kx2e5x is a particular solution of the differential…

Q: Why is it necessary to get acquainted with the sigma notation's properties?

A: Yes, it is necessary to get aware of sigma properties . It help mathematics to improve itself.

Q: The function f(x) = x² + 1 is Bijection from R to R

A: This is a question from the function.

Q: PROBLEM NO. 11 Given: x-64=0 Find the secondary root. A) 1 + 1.732j B) -1 + 1.732j C) 1 - 1.732j D)…

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Q: -1 1 1 1 1 1 −1 1 1 1 -1 -1 1 -1 1 and B = -1 1-1 1 -1 -1 1 5 k -1 1 5 k h all values of the…

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Q: Use Cauchy's theorem or integral formula to evaluate the integrals. sin z dz T dz, where C is the…

A: Using Cauchy's theorem or integral formula we evaluate the given integrals.

Q: dy Consider the equation = ay — y² = y(a — y). dt a) Consider the cases a 0. In each case find the…

A: Consider the given differential equation, dydt=ay-y2=ya-y As we know that the critical points are…

Q: in fuzzy graph What is the fuzzy forests ? And give an examples

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Q: 2. The matrix A has eigenvalues -2,-2, and 1. Find 3 linearly independent eigenvec- tors for A. Show…

A: As per our guidelines we are supposed to answer only one question. Here question 2) answered.

Q: An unmanned rover must be routed to visit four sites labeled A, B, C, and D on the surface of the…

A: Given- An unmanned rover must be routed to visit four sites labeled A, B, C, and D on the surface of…

Q: EXERCISE 2.2 Derive the expression of the Bezier curve for the four points Po = ( = (0, 0, 0), P₁ =…

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

Q: the solution of the givin DE dy dt = =t+y, y(1) = 0, at t 1.2, h = 0.1 Yexact = 0.2428 (find the…

A: The given problem is to find the solution of given differential equation at given point by step size…

Q: Consider the market for lollies where if the price per lolly is $4, total market demand for lollies…

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