9. Let P(x) = 3x² – 5x³ + 7x* + 3x5 be the fifth-degree Maclaurin polynomial for the function f about x = 0. What is the value off"(0)? (A) -30 (B) -15 (C) -5 (D) = (E) 긍 6.

Q: Interpolate the function f(x) = ev3 on [-1, 1] with a second degree polynomial by using the zeros of…

A:

Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

A: Let the polynomial is  fx=αx-15x--23x-4=αx-15x+23x-4=α5x-153x+22x-4 Coefficient will be integer if α…

Q: 10. Write a 3rd degree polynomial function with zeros: -4, 6i

A: Given: Zeroes of a polynomial which are -4, and 6i. The complex roots always lie in pairs, if one…

Q: 4: You are to choose a non-polynomial function, an interval, and six points at which to interpolate…

A: Given: Choose a nonpolynomial function  To find the Lagrange form of interpolating polynomial and…

Q: Suppose f(x) is a polynomial of degree 72. Can f(n)(0)=1 for all n>1. If it can give an example of…

A: Given that f(x) is a polynomial with degree 72.We have to see whether fn(0)=1 for all n≥1.

Q: 5. Find the asymptotic behavior of the polynomial f(x) = -x"+4æ® + 2x³ – x³ + 10x? – 12x – 10 (i.e.…

A:

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions as : n…

A: Since 1 and i are the zeroes of the polynomial, therefore

Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

A:

Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

A:

Q: you are asked to create a fourth degree polynomial function with real zero of -2 and 2 both with a…

A: We have to find

Q: 2. What is Pia first-degree polynomial function whose value and slope agree with the value and slope…

A: “Since you have asked multiple questions, as per authoring guidelines we will solve the first…

Q: 4. Use the Intermediate Value Theorem to show that the polynomial function f(x) = x" +8x' – x´ +2…

A:

Q: 1.The graphs of f(x) = (x+3)(x- 4) and g(x) = (x+ 3)(x- 4) Which graph represents which polynomial…

A: Given that:

Q: The 2nd degree polynomial that interpolates to f(x): = 2cosx - sinx at x = 0, x = π/2 and x = π is…

A:

Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…

A:

Q: 7. The fourth-degree polynomial f(x) = 230x* + 18x + 9x? – 221x -9 has two real zeros, one in [-1,0]…

A: As per the guideline, I am doing the 1st method only. Kindly repost the others separately.   Secant…

Q: Q-3: Plot the zeros of each polynomial on a line together with zeros of its first derivative. 1. y =…

A:

Q: If f is a polynomial function and f(a) and f(b) have opposite signs, then there must be at least one…

A: We know that if fx is a polynomial function and fa and fb have opposite signs, then there must be at…

Q: 13) Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given…

A:

Q: .5) a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x2

A: Given ,            f(x) = 1-3x+3x²

Q: 9) Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given…

A: Here the given function  gx=3x3-10x+9 ; -3, -2 The given function is continuous in the given…

Q: sketch the polynomial function by finding all the critical values. g(x)=x4-4x3-15x2+58x-40

A: given, g(x)= x4-4x3-15x2+58x-40 we have to find the all critical values and sketch the polynomial…

Q: 7. find a polynomial function with real coefficients that has the given zeros: 0, 3, 2+i

A:

Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: The polynomial function f has exactly one positive zero. Approximate the zero correct to two decimal…

A:

Q: Let s(t) be the distance of a truck to an intersection. At time t = 0, the truck is 60 m from the…

A:

Q: estimate the value of x correspond to f(x) = 1.6 Using cubic interpolating polynomial together with…

A: Given data is x 1 2 3 4 f(x) 3.6 1.8 1.2 0.9 The value of x corresponding to f(x) = 1.6…

Q: 8. Determine algebraically the polynomial function that passes through the points below.

A: Given,

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions as : n…

A: the given conditions are: n=4; 2(with multiplicity 2) and 3i are zeroes, f(0)=36 we have to find an…

Q: The Taylor polynomial of degree 100 for the function ƒ about x = 3 is given by (x – 3)100 50! 2n…

A:

Q: h(x) 36千 27 18- 9- -5 -4 3-2 -i 0/1 2 4 5-x 3 4 6- -18+ 27+ 36+ -45+

A:

Q: 1. Find a polynomial of degree 3 whose zeros are -4, -1, 2 and y intercept 16.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Polynomial of lowest degree with zeros of -2 (multiplicity 2) and 3 (multiplicity 2) and with f (0)…

A:

Q: Find a polynomial f (x) of degree 4 that has the following zeros. 7 (multiplicity 2), –3, 0 Leave…

A:

Q: show that the polynomial below has a root between 0 and 1.

A: Given f(x)=2x3-11x2+18x-6 to find the root of the polynomial which lies between 0 and 1

Q: Let f (x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity…

A:

Q: 8. Find a fourth degree polynomial function with zeros 4,-2, 51, and -3i.

A: Que  Ans:     P(x) is 4 degree polynomial          with   roots 4, - 2 , 3i,  - 3i Implies that…

Q: Which type of polynomial satisfies f ,,, (x) = 0 for all x?

A: Let f(x) be a polynomial such that f'''(x)=0 for all x Integrating both sides ,we get Again…

Q: If the leading coefficient of an odd-degree polynomial function is positive, then the function…

A:

Q: What is the end behavior of a polynomial function of degree 7 with leading coefficient -2?

A: Given: The polynomial function have a degree 7 and leading coefficient is -2. Concept used: The end…

Q: 5) Write a rule for the 6th degree polynomial 8(x) pictured at right, whose only roots are -5, -2,…

A:

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

A:

Q: 9. A polynomial function has a point of inflection at (a,0) and a point of tangency at (b,0).

A:

Q: 4) Polynomial of lowest de 1) and with f (0) = -18

A:

Q: 6. Give an example of a polynomial function that has each of the following end behaviours: a) As…

A:

Q: The graph of a polynomial function will appear to bounce off the x-axis at zeros that are of an even…

A:

Q: Find a polynomial fuction f(x) of degree 3 with real coefficients that satisfies the given…

A: Using the factor theorem: If x = a is a zero of a polynomial P(x), then (x-a) is a factor of the…

Q: 4.1. Determine an equation for a polynomial function with zeros -4 (order 4) and 2 (order 3).

A: To find the equation of polynomial with zeroes as -4(order 4) and 2(order 3).

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Given  zeros of polynomial x= -1 and x= 4

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.