(1+x) Pn (x) dx = let Pn (x) be legendre polynomial of degree n>1, then, .a 2n +1 .b .C 1 2n +1

Q: (2x+1)P,(x) dx = let p, (x) be third degree legendre polynomial , then -1 2 a O 1.c0 -1do

A: Option (b) 0 is correct.

Q: Let p(x) be a polynomial that is divisible by (x-a)n where n∈ N and n >= 2. Prove that p'(x) is…

A: Here, given that the polynomial p(x) is divisible by (x-a)n. So, p(x)=(x-a)nq(x)...(1) Where, q(x)…

Q: dx -= In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) A + - B 6. + 3 D + 6 + -15 -15 -15

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Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Evaluate the expression (In (3.34)- tan (61.010)-2)/(5.011e0.37 +1)

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: Write the polynomial 6x2 + 5x +7 as alinear combination of Legendre polynomials and use it to…

A: I will use the orthogonality of legendre polynomials.

Q: attached

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Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

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Q: Find the domain of v. v (x) = x + ln(7x - 4)

A: Find the domain of v. v (x) = x + ln(7x - 4)

Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: Find Ao, A1, and A2 in rewriting the function of f(x)={* x20 in terms of Lagure polynomial, 00 S(x)…

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Q: The polynomial that passes through the following (x, f(x)) data 18 22 24 f(x) ? 50 246 is given by…

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Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: A toy rocket is shot into the air. Its height, in meters, after t seconds is given by h(t) = -4.9t²…

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Q: Let xo < x1. Find a second degree polynomial P(x) such that P(xo) = fo, P(x1) = f1, and P'(xo) = fó-

A: Consider a second degree polynomial in x as: P(x)=ax2+bx+c                                     ..(1)…

Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

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Q: 2. If m < n, show that mPa(x)dr deduce that r* P6(r)dr = 0. = 0, where Pn(x) denotes the Legendre…

A: We have prove the given problem.

Q: Find Ao, A1, A2, and A3 in rewriting the function of f(x)=- x20 in terms of Lagure polynomial, x<0…

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Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

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Q: Find f 1+x² (1-x²)√1+x4 dx

A: ∫1+x21-x21+x4dx Note:- As per the company's guidelines, we are supposed to solve the first question…

Q: The zeros of the polynomial function f(x)=x² – 2x² – 15x are: a. {-5,–3,0} . b. {-3,5} . c. {-5,3} .…

A: We have the given function as fx=x3-2x2-15x On solving further by making factors, we get the result…

Q: Q5) Find the root of f(x)= 5 sin(x) + ex² by using bisection method take a= -1.25 and b= -1.0 for…

A: Given, fx=5sinx+ex2. Here, a=-1.25b=-1.0 Now,…

Q: 3x² -7x+8 Let f (x) = Find f' (x) sin (5x²+9x-6) mil nction/that sati

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Q: F= = 2KX Ex (1 (1-1 t FOX 11 + x ² 2 L2 3 ( ) x ² assume that d L ... ( ١ ) (2) is very small

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Q: local maX

A: From the given graph of polynomial function y=fx, The graph of fx intersect x-axis at x=0, x=1 and…