If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-3)g(-3) + f(0)g(0) + f(3)g(3) defines an inner product in P2. Use this inner product to find (f, g), ||f ||, ||g|| for f(x) = 3x + 4x +7 and g(x) = 2x? – 6x + 4. (f,g) = || || = llg||

Q: Find (F÷a) an FIx)= 14,+2

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Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: find the inverse of

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Q: 51+* + 1 y = 5*

A: Given: y=51+x+15x     ⇒   y=51+x5x + 15x                =5+ 15x       y-5=15x           5x=1y-5   x…

Q: Find two positive real numbers such that they add to 40 and their product is as large as possible.

A: Our Aim is to find two positive real numbers a and b such that they add to 40 and their product is…

Q: find the vlaue of x 12 16

A: The secant-tangent rule describes the relation between the secant and the tangent that are drawn…

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

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: Explain the other notation which is commonly used for ak in the Newton form of the interpolating…

A: The Newton interpolation polynomial are calculated as: \

Q: Explain the problems with the Lagrange form of the interpolating polynomial?

A: Lagrange polynomials are used for polynomial interpolation.

Q: Find x and y such that,  77815x - 8216y=(77815 , 8216

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Q: find all real such that 12x-11>x

A: The inequality can be calculated using absolute values. The absolute value function takes a positive…

Q: Use Newton’s Divided Difference Formula to interpolate f (1), if the polynomial has given points…

A: We have to interpolate f(1) using Newton's Divided Difference Formula.

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: S(*-2:) (12x² -8) đx. (b) Integrate the expression of

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Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

Q: Let f {(0,-3),(9,4),(-6,9)} and h={(-6,4),(-3,9)}. Find fo h. foh= (Use a comma to separate ordered…

A: The given functions  and .The objective is to find the composition function .

Q: Calculate the triple product ā · (b x c), where ā =,b=, and č=.

A: Given vectors  a→=2 , -4 , 1b→=0 , 3 , -1c→=5 , -3 , 3

Q: find the inverse of Laplzee p3+P

A: Some Laplace transform formulas: L-1ss2+a2=cosat L-11s=1 L-1as2+a2=sinat

Q: Define identity properties

A: Here we have to define the Identity properties:-

Q: DO NOT include spaces in between characters. * Compute g'(2) if g(x) =10**-2* 16 Your answer

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Q: Define the Newton form of the interpolating polynomial?

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Q: Express as a polynomial.

A: given: a-ba3+a2b+ab2+b3 we have to express it as a polynomial.

Q: Explain why the Theorem of Pappus is useful.

A: To Explain: Why the Theorem of Pappus is useful.

Q: Let f(x) = x^2 + 8x a. Express f in standard form by completing the square. b. Find the vertex of f.…

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Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.