2. Identify all the root(s) of f (x) = (x- 6)²(x + 2)² %3D a.) -6 with multiplicity 1 multiplicity 2 b.) 6 with multiplicity 1 e.) -6 with f.) 6 with multiplicity c.) -2 with multiplicity 1 multiplicity 2 d.) 2 with multiplicity 1 multiplicity 2 g.) -2 with h.) 2 with

Q: [ 1 If A= -1 0 find x and y such that (xI +yA) = A

A:

Q: Find the absolute maxima and minima of f(x) = (7cos(x))/(8+4sin(x)) in the interval 0 ≤ x ≤ 2pi.

A: To find the absolute maxima and minima of f(x) = (7cos(x))/(8+4sin(x)) in the interval 0 ≤ x ≤ 2pi.

Q: Find a point c satisfying the conclusion of the MVT for the func y(x) = 2e* on the interval [0, 5].…

A:

Q: Let f(x) = x2 + bx + c, b is negative odd integer, f(x) = 0 has two distinct prime number as roots,…

A:

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

A:

Q: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: The function f(x) = x -x2 - x- is graphed in 11 %3D 4 the xy-plane above. If k is a constant such…

A:

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: Prove that v = In (x- 2)^2+(y-N)^2 is harmonic in every region does not include the point (2,N) and…

A: Given v=lnx-22+y-N2 where N=44. So, v=lnx-22+y-442                                    ........1 To…

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: 2. Find all the critical numbers a. f(x) = 2secx (0,2n) b. g(x) = (x² – 4)3

A: Critical Numbers : Critical numbers are the numbers where the function is defined and its derivative…

Q: Consider the problem maxx [-(x - 4)]² subject to x21. Use Thus the Kuhn-Tucker conditions to find a…

A: We are given the following problem.       maxx -(x-4)2       Subject to x≥1 Let us simplify the…

Q: 1: What happens to the above if the root r has a multiplicity m?

A: It is given that, the root r is a root multiplicity m that is fx=x-rmgx where gr≠0

Q: Find a 5 with real coe ffients that satisfies the aiven conditions. zeros of a, 5and-3; P)=4…

A: We have to find the polynomial of degree 3 with given condition.

Q: 1 Find the absolute maxima and minuma x²-2x4+ bunded by y= x², y=t, the closed negion on %3D…

A: Given that, f(x,y)=x2-2xy+y Take the derivative for x, fx=2x-2y Take the derivative for y, fy=-2x+1…

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 8e* on the interval…

A: Let the given function is  y(x)=8ex  on the interval [0, 9]

Q: 6 2, find the following. - V (gof)(x) 2√2(1-2x) X (b) the domain of (gof)(x) in interval notation −…

A:

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: 4. Prove that if f(x) = aox" + a,x"-1+ ...+ an-1x = 0 has a positive root x = xo, then the equation…

A: Roll's theorem: If f is continuous function on [a, b], differentiable on (a, b) and f(a) = f(b) then…

Q: Employ the Parabolic Interpolation method to find the maximum of the following function using these…

A: Given: x0=-2, x1=-1, x2=1 f(x)=-x^4-2x^3-8x^2-5x

Q: Find all values of n such that y = xn satisfies x2y" - 12y = 0

A: To solve the equation x2y''-12y=0, we first need to find y''. y'' can be obtained by differentiating…

Q: Find extreme value(s) of z = 2x¡ + x,xX2 + 4x3 + x,x2 + x} + 2

A: Consider the provided question, According to you we need to solve only part (d). (d)

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

A:

Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

A:

Q: An arbitrary point x of 0.1 is chosen. Since it is known that x> = 5, what is the existence of x> =…

A: x is an arbitrary point of (0,1)  and x ≥0.5x≥78=0.8

Q: Find a polynomial function p(x) of degree 3 with real coed fiends that satisfies the given…

A:

Q: Show that when x increases from 1 to 1.25 and when it increases from 2.75 to 3, the value k of grows…

A:

Q: Suppose that K, L, M, and N are four approximations of the unknown root r of function f such that…

A: Given: Suppose K,L,M,N are four approximations of the unknown root r of function f. since r is the…

Q: Verify that the function satisfies the three hypotheses of Rolle as a comma-separated fist.) x) = 3x…

A:

Q: The base of a three-dimensional figure is bound by the graph y = sin(x) + 1. Vertical cross sections…

A: Let a be the length of each side of a square. Then, the area of the square can be calculate by using…

Q: @ f(x)= x²-3x-4 2 @ f(x) = x² - 4x +3 Show that whether f(x) reduceable Poly or not

A: The given problem is solved below in detail.

Q: Find the value of m that makes: Show that the equation  xex-1=0 has a unique solution on [0,1].

A:

Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

A:

Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: 1d. Show that the given equation x- In xX= 0, has a root in the interval [4, 5].

A:

Q: 3) Prove the following statement using the Intermediate Value Theorem (IVT): 2ª + 3* = 4* has a…

A:

Q: :Use inverse matsix (by Gauss Jordan an Elimination) to solve the syálem 2x + By +3 = - 1 %3D 2x…

A: Consider the given equations 2x+3y+z=-13x+3y+z=12x+4y+z=-2 The given equation can be written as AX=B…

Q: 4. Prove that if f(x) = agx" + a,x"-1 +..+ an-1x = 0 has a positive root x = xo, then the equation…

A: Note that f0=0 and that fx0=0. So using mean value theorem there must be some 0<λ<x0:…

Q: 5. Find all pairs (m, n) of positive integers such that y(y(nm)) = n, where p is Euler's totient…

A:

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: Suppose three similar geometric figures are constructed off the three sides of a right triangle in…

A: Consider a right triangle with the length of the altitude a, the length of the base b and the length…

Q: 1. A bowl contains 10 red and 10 yellow balls, how many balls must be selected to ensure 5 yellow…

A: To solve this type of questions we consider the worst case that is  after taking all red balls we…

Q: Find all triples of integers (x, y, z) that satisfy x² + 2y² = z2.

A:

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: 10. Find all of the discontinuities that exist for g(x) = 2*+3x-4 Show any work required to %3D x+1…

A:

Q: 3 By applying the Intermediate Value Theorem choose the interval over which x4 = 7x3 - 5 will have a…

A: The given problem is to find the interval for the given function that which the intermediate value…

Q: 7. Use the Intermediate Value Theorem (IVT) to show that there is a root of the equation In r = 3 –…

A: We can use intermidiate theorem in order to solve the given problem.

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 2e* on the interval…

A: Solution: The objective is to find a point c

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.