Find second order partial derivates of the following function

Q: 4. Find the partial de x2+2x-3

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Q: x5 – 4.x + 7 (x² – 4)(x² + 2x)(x² + x + 1)² -

A: The given rational function is x5-4x3+7x2-4x2+2xx2+x+12.…

Q: 8. Construct a natural cubic spline that interpolates the function f(x) = 1/(1+ x²) at x = -2, –…

A: Let the cubic spline polynomial of f(x) be H(x). Then Hx=fa+fa,ax-a+fa,a,bx-a2+fa,a,bx-a2x-b…

Q: a- Obtain the inverse z-transform of the function 100z F(z)= (2+1)(x+2)(2+3) using partial fraction…

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Q: write the form oF the partial deco mpOS1tion of the determine the the coe fficients. function.DO not…

A: 1x4-256=1x4-44=1(x2)2-(42)2using a2-b2=(a-b)(a+b) formula1(x2)2-(42)2=1(x2-42)(x2+42)again using…

Q: Find the partial fraction decomposition of the rational function.

A: To find: The partial decomposition of 8x-32x2-x. Calculation: The partial decomposition of 8x-32x2-x…

Q: write out the form of the partial fraction decomposition of the function (as in this example). Do…

A: The objective is to find the area of the surface obtained by rotating the arc of the curve y=9-x2

Q: 22 The partial fraction decomposition of can be written in the form of (x – 1)(x + 1) f(x) 9(x) x…

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Q: x² - x xp x² + x + 1

A:

Q: Expand the following rational function using partial fractions. Do not integrate. 1 1? – 1

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Q: Use a partial fraction decomposition to represent the function f(x) rational functions.

A: answer is in next step

Q: Expand the rational function 16 / (x2+x+2)(x−1)2 into partial fractions.

A: We have to

Q: Write out the form of the partial fraction decomposition ofthe function (as in Example 6). Do not…

A:

Q: Determine a partial fraction decomposition for the function 30x / (x+1)(x−2)(x+3).

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Q: Write the form of the partial fraction decomposition of the function. Do not determine the numerical…

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Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A: Given that the equation x-20x2+x-20. Determine the form of the partial fraction decomposition of the…

Q: Set up the partial fraction decompostion of 2x^3-1/(x-1)(x+2)(x^2+1)^2

A: Given the partial fraction 2x3-1(x2+1)((x+2)(x2+1)2.We need to set up the partial fraction…

Q: A natural cubic spline S for a function f is defined by +3 x² x 3 + 3 2 1≤x≤2 2≤x≤: 3≤x≤ 5(x) = - 12…

A: Given, A natural cubic spline ,s for a function.…

Q: By using partial fraction and 2nd shift theorem, show that, 3 3 L-1, ls(s² + 4) -H(t – 4) –H(t –…

A:

Q: Write out the form of the partial fraction decomposition of the function: (x^2)/x^2+x+6

A:

Q: Express the rational functions as partial fractions: 1 (x - 1)(x² + 1)

A: We need to express the rational functions as partial fractions.            1x-1x2+1

Q: Write the form of the partial fraction decomposition of the function (as in Example 4). Do not…

A: The denominator of the fraction consists of two factors: 1. (x-5) with multiplicity 2 2. (x+7)

Q: Find all first partials and simplify each one for the function z=2y^2sqrt(x)

A: To find the all first partial derivatives.

Q: write the form of the partial frachion decomposition of the rational values of the constents.…

A:

Q: Minimize the following function using the conjugate gradient algorithm

A: Given: fx1,x2=12x1x23112x1x2-x1x273

Q: Write out the form of the partial fraction decomposition ofthe function (as in Example 6). Do not…

A: For partial fraction decomposition order of numerator must be less than order of denominator.

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A:

Q: (h) Write down the Lagrange's polynomial through (x), fo). (x1, f1), (x2, f2). Hence express 3x²…

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Q: Express the partial fraction decomposition form of the function A) x2 + x + 72

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Q: х4 + х3 + x? — х+1 x(x² + 1)²

A: To find out the partial fraction decomposition of the function given.

Q: Write out the form of the partial fraction decomposition ofthe function (as in Example 6). Do not…

A: We have to write in partial fraction decomposition of the function: x4x2-x+1x2+22 We know the…

Q: show that g(x) = (1/2)x has a unique fixed on [0,1]

A:

Q: Determine the global maximum and minimum function a)f (x): x² + 1 in the intervals [0,2]

A:

Q: Write out the form of the partial fraction decomposition ofthe function (as in Example 6). Do not…

A: The given function is xx2+x-2. First factorize the denominator as follows.…

Q: Find the partial fraction decomposition of the rational function.

A: It is observed that for the function 2(x-1)(x+1),the factors are x-1  and x+1.The partial fraction…

Q: Find the partial fraction decomposition of the following rational function.  f(x) =6/x^2+3x-28

A:

Q: 1 19. x(x² + 1)

A: Solving the problem by finding the partial fraction decomposition.

Q: Find the global maximum and minimum of the function on the given interval:f(x)=x2−2x+5,x∈[−1,4].

A:

Q: Find the partial fraction decomposition for the rational expression. 5x-3 x(2x + 1)? 5x-3 x(2x² +…

A: To find the partial fraction decomposition

Q: Which of the following functious has the partial fraction decomposition a2 1 ² =

A: For finding function from partial function we will further make function from given partial function…

Q: Minimize the following function using the conjugate gradient algorithm 1 f(x1, *2) =(*1 (X1 With a…

A: Given: f(x1,x2)=12x1 x23112x1x2-x1 x273

Q: Let f(x)= x+1 1³ - 2x² + 1

A: Solving the problem by finding the fraction from the expression.

Q: 6. (a) + 1'

A: We have to find out

Q: Let F(x) -4x +27x2 - 42x+20. Find the global maximum value of F(x) for a in the closed interval [0,…

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Q: 22 The partial fraction decomposition of can be written in the form of (x – 1)(x + 1) g(x) x +1'…

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Q: (a) Deduce in the form of a Partial fraction. (x2-x+1)(3x-2) (b) Limits of functions are evaluated…

A:

Q: x² x² + x + 20

A:

Q: Find the global maximum and minimum of the function f(x)=√3−2x on the interval [−3,1).

A:

Q: 1 f(x) = (x – 8)(x + a)

A:

Q: a)f(x) = 3(x² – 1)° in the intervals (-1,2)

A: I have solved using derivative test

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.