Find a first-order L²-approximation for the following equations f(x) = sin x f(x) = e-3x 0≤x≤1 0≤x<∞0

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Q: If a polynomial function p has an x-intercept -1, then p(x) is divisible by

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

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Q: 5. Find the equation of the straight line passing through (3,-5) and parallel to the line joining…

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Q: dx + AIX y = cos x, y(n) = 0

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Q: 2. In both parts, full marks will only be obtained if exact answers are given in terms of . √2 etc.…

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Q: 1) Let A have a QR-factorization where Q= would be: E 0.5 -0.5 0 0.5 -0.5 0 0.5 0.5 0 1 -5 -45 1 10…

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Q: Statement 1 - If you study hard, you get good marks Statement 2:- If you get good marks, you get…

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Q: Question 4. (1) [x³² √x² + 4 dx. X3 sin (In x) X (ii) S -dx. Evaluate the integral: (iii) Choose a…

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Q: 2y" - 5y' + 3y = 0, y(0) = 3, y'(0) = -4

A: Given equation is 2y''-5y'+3y=0   Also given y(0)=3 and y'(0)=-4

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Q: My home uses two light bulbs. On average, a light bulb lasts for 100 days (exponentially…

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Q: 2. Suppose you start a business making and selling earrings. Your cost to make each pair of earrings…

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Q: Find the solution set of the following. 2(1 + cos x) sin x -. tan X 2 x = [0, π]

A: tan(x/2)=2(1+cosx)/sinx tan(x/2)=((2sin(x/2))^2)/2sin(x/2)cos(x/2)        where 1+cosx=2(sin(x/2))^2…

Q: Q3) For T (x,y,z) = (2x + y, x – y) find: a) The image of v = (2,1,4) b) The preimage of w = (-1,2)

A: As per our guidelines we are supposed to answer only 3(a) and 3(b). For Q4 please repost it.

Q: (6) A loan of $20,000 is to be repaid in uniform monthly payments over 3 years. If the interest is…

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Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives fr and fy at the…

A: Given: fx,y=x-1·y13 We have to determine whether fx,y is differentiable at the point x,y=1,0

Q: 22. Solve the following Dirichlet problems: (a) V²u = 0, u (x,0) = x (x - 1), u (0, y) = 0, 0 < x <…

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Q: K Use the Principle of Mathematical Induction to show that the following statement is true for all…

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Q: Let G be the set of all triples of the form (k1, k2,1) or (k1,K2,-1), where the ki, i=1,2 are…

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Q: 6. For how many values of n will a regular n-sided polygon have interior angles with integral degree…

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Q: Use high-accuracy differentiation formula O(h) to estimate the first derivative of f(x)=log.x.…

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Q: Let f(x) = (x+1) arctan(1-2x) + f(t) dt) Which of the following statements are correct? I. f'(0) +…

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Q: a) Use Picard's theorem to prove the following IVP has a unique solution in its domain: y' = 1 + (t…

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Q: Let f(x,y,z)=x^(2)y+y^(2)z.  Find the exact value using the Fundamental Theorem of Line Integrals,…

A: Given That :   f(x,y)=x2y+y2zr(t)=sinπ2t ,3t+log(2-t),ecos(πt) a=0,b=1 To find : exact value using…

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Q: Evaluate (2x+2y)ds if the curve C is given by F(t)=(2t²)ī +(1²)j, 0≤t≤1.

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Q: let f(x) be a function f:[0,1]→[0,1], f(x)=−4x(x−1). Let g(x):(−∞,∞)→[0,1] be a function such that…

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Q: Please go though every step and do not use a texblook solution. Why is the gcd(n-1,n)=1? why is n-1…

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Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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Q: 4 (1) Evaluate the following summation: Σ i + 2 i=2

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Q: Solvex (az + √2) dx − y(az + √2) sin (ay²) dy + (az √2) dz = 0

A: Integrate both sides