The domain of the function g(t) = vt – 8 is O (8, 00) O [8, 0) O (-∞, –8) O R O R-{8}

Q: Let f € L'(0,1). Assume that f(t)t2"dt = 0 for all n f = 0 a.e. 1,2,3,.... Prove that %3D

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Q: If pN(x) is the polynomial of degree N which interpolates f(x) cos(3x) at N+ 1 uniformly spaced…

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Q: If the moment-generating function of X is M(t)= e, then the moment-generating 3t function of Y=1+-X…

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Q: 1- Prove the following relations: ag = (x – t) g(x, t) at (1 – 2xt + t?)- (1) (1 – 2xt + t?) ag = t…

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Q: Let ww. f(x) = x² + Mx a) Approximate to f' with step size h = 0.1 by using central difference…

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Q: af Q1: a) Use the chain rule to calculate for the function f(x, y, z) = 3x² - 3y + 4xz², x =…

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Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

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Q: 1. Use a local linear approximation of the function f(x) = Vr cos[(V2x)7] approximate v3.98…

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Q: 25-let F(xs.2)=x-x22 @ Find VF 6 write the equution of tngent Plame to the at Paint (2,1,1). Find…

A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: 6. Let 1 f (x) - cos x + sin(2x), x E [0, 1] 2 Find the least squares polynomial approximation of…

A: Let fx=12cos x-sin2x, x∈0,1. To find quadratic fitting  fx≈P2x=a0+a1x+a2x2 Consider, s0=∫011dx=1

Q: Find the residue of the function f(z) = 1- e2z at its pole. z4 |

A: The given problem is to find the residue of given complex variable function at its pole, we can use…

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: 2) Find the 6h-order Taylor polynomial of the function f(x)=e*, centered at x= 0.

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Q: Find the degree 3 Taylor polynomial T3(x) of function f(x) = ( – 5x + 276)7 4. - at a T3(x)

A: We need to find 3 degree Taylor Polynomial of the function f(x)=(276−5x)54 at a=4 so using Taylor…

Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

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Q: Find the order of growth k of the infinitely large function 3. f(x) 3a + In z with respect to g(a)…

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Q: 20. Let yapp (x) be a polynomial approximation, involving only one coordinate function, for the I(4)…

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Q: 6. Find the Wronskian for the set of functions {e¬x, xe¯*, (x + 1)e¬*}.

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Q: 9- The general solution for the PDE (DD, + D,D-12D =0 is a. u(x, y) = G,(x)+G,(x+y)+G,(x-y) b. u(x,…

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Q: The moment generating function of X is defined by M(t)=E(etx) صواب İhi

A: True.

Q: Q3: Find the Wronskian for the following solutions. Y, = 1, Y =In

A: Wronskian= 112ln1+x1-xd1dxddx12ln1+x1-x= 112ln1+x1-x01x+11-x=1x+11-x

Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

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Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

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Q: t²x"" +2tx" + x' +2022x 0 for t> 0. If their Wronskian satisfies W(2) = 20, then find W(t) for all t…

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Q: Find the degree 3 Taylor polynomial T3(x) of function f(x) = (7x – 19)*/2 - = 4, T3(x) at a =

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Q: Consider the following first-order ODE: d = (1+2x) √9, x = [0, 1], y (x = 0) = 1 Using step size of…

A: consider the following first order ODE dydx=1+2xy with x=0,1 and yx=0=1 claim- use step size h=0.05…

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Q: (b) For f(z) find the residue of f (z) at the singular point (z+1)2(z2+4) z = -1

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Q: Find T4(x) Taylor polynomial of degree 5 of the function f(x)=cos(x^3) at a=0

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Q: Find the residues of the followings functions at z = 0: (1) (z2 + 1)/z

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Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 107 dx 2.316 10-11 1.22-10 Using trapezoidal and…

A: The integration can be calculated using the numerical method. The formula for the trapezoidal rule…

Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)

Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

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Q: -Find the least squares approxtmation polynomial of degree two for the continuous function f(x), (x)…

A: Least square method to approximate polynomial: Least square method to approximate the two degree…

Q: 3. Let g(x) = V10- cos(x) +3x. %3D 3.1. Find g'(x). 3.2. Find the linear approximation to g(x) at x…

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Q: Find the residue at z = 0 of the function 1 / (z + z^2)

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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Q: 38.. Find the third Taylor polynomial at 0 = x for the given function. f(x)= e10x 1000 а. 1+20x +…

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Q: The generating function w (x, t) = (1– 2xt + t2)-1 is given. (a) Show that it satisfies the identity…

A: Note: Since problem 7 is not given which is needed to solve part b, we will solve part a. Given:…

Q: Find T3(x): the Taylor polynomial of degree 3 of the function f(x) = cos(6x) at a = 0.

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Q: 1. Determine the discrete least squares trigonometric polynomial S2 (x) on the interval [-T, T] for…

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Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y = x' on the interval 0 < x s 2. Write a…

A: Differentiate the expression of the slope with respect to x. For any value of x in the interval…

Q: Show that the functions In x , In(x2) linearly dependent (0, co) are on

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Q: 7. Let f(r) = 2r - 4r? + 1. %3D (a) Find any critical points (c, f(c)) of f(x).

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Q: 17. Find the decomposition of the function h(x)= Vx² - Jx two different ways. %3D

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Q: The function g(x) = (1/2) x - (3/2)x + 2 has two fixed-points x, = 1 and x2 = 4, then the functional…

A: Here we find the limit of the equation.

Q: Q2/ Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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