Chooes In legendre polynomials Porm the bassis of chebyshev Polynomials Te CX)= ®늦 (4L201 -Locu) + (4 Lz(x) +Lo (x) 3

Q: . a. Approximate y = e# using the Taylor polynomial P3 (æ) of y = e at 0. а.

A: Given y=ex at 0

Q: Where does the polynomial y = x² + 3x + 2 cross the x-axis? O (1, 0) and (0, 1) (1, 0) and (2, 0)…

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Q: A polynomial expression is given. 3z (zy) 21'y Which is an equivalent form of the expression? 3y 3y

A: Explanation of the answer is as follows

Q: Also, our definition of the first 4 Legendre polynomials is: 1 Po(x) V2 P1 (x) = V5/2 (1 – 312)…

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Q: A section of the graph of a polynomial function with integral coefficients is shown. Which of the…

A: A function curve in graph, where it cuts x axis is a root  of the function.From the given graph the…

Q: different. To show that all the roots of Pn(x)=0 are

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Q: Consider the function g(x) 1. Show that 1 (1 - x)² (1-x)². 1 + 2x + 3x² + ... + (n + 1)x² + n+ 2…

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Q: 7. (a) Find a cubic polynomial, q(x), such that q(0) = cos 0, q = COS = coS q (T) = cos ㅠ. 3 3 (b)…

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Q: 3. 4. X- ex t ちメ+1 メ+2

A: Topic = Algebra

Q: 9. For the graph below: a. Describe the end behavior. b. What are the factors of the polynomial…

A: We have to find

Q: Electric resistance in a copper wire changes with the temperature of the wire. If C(t) is the…

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Q: factor x as a product of three linear polynomials in Z/30Z[x] by using Chinese remainder theorem

A: Ans- To factor x as a product of three linear polynomials in Z/30Z[x], we first need to factor 30…

Q: 11. The Hermite polynomials, H,„(x), satisfy the following: į. = Se-**H„(x)Hm(x) dx = \T2"n! 8,m:…

A: To prove: ∫-∞∞xe-x2HnxHmxdx=π2n-1n![δm,n-1+2n+1δm,n+1] Proof: Take the LHS ∫-∞∞xe-x2HnxHmxdx and…

Q: A. Classify the following polynomials as to degree. 1. 4x2 + 3x - 7x + 8 6. 3 + 3x? 2. x + 2x - 5 7.…

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Q: the lakrang. 3 foxy 2 2 7 True Erort

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Q: Show that 1.3.5... (2 n – 1) (i) P2n (0) = (– 1)" (ii) P2n+1 (0) = 0. 2.4.6 ... 2 n

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Q: Factor x12 - 1 as a product of irreducible polynomials over Z.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: nsing Eisenstein's criterior of isreducibility show that the polynomiel B p (W) = 3Es lon+0 i's an…

A: The condition for the polynomial to be irreducible is given below

Q: approximate the solution to:   y' = x2 + y;  y(1)=1. y1(x) ______________     a) y= 1-x+1/6 x3  b)…

A: Hello: im solving only 1 part of this question  Note that this is a multipart question having two or…

Q: (b) Now consider the general case of n+1 data points {(xi, f(xi)}? _o and a polynomial p given by…

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Q: Q2/ Fit Polynomial and & @ д @T х 20 Lo Ro T-X 1-50 csy 0.125 0.128 Q 134 0.144 0115 F

A: To solve the system of equations, we can represent it in matrix form:\[\begin{bmatrix}1 & T_1…