13) Use the Intermediate Value Theorem to show that the polynomi: zero in the given interval. g(x) = 3x2 – 7x – 4; (2,3)

Q: Solve the following inequality graphically in two-dimensional plane:y < – 2

A: We first draw y=-2 line

Q: M=N

A: answer is in next step

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A:

Q: Show that there is a solution to the following equation in the interval (2,3). (Hint: Use the…

A: Since there are two questions posted, we will answer the first question (1). If you want the second…

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

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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: 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 the set A = {x ∈ R | 3x + 2 ≤ 0} has a maximum

A:

Q: 4. Use the algebraic description to find the image of AMNO). (x, y) → (x+ 2,y- 3) -3 21

A: From the figure, we see that M(-2,4), N(-3,1) , O(-1,0).

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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: Use Eceler's formula to express the function:7x) =xarsinx as the sum of a real andd imaginary…

A:

Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

A:

Q: 8. Express as a polynomilal. Arrange your answer from term with highest degree to lowers degree *…

A: SINCE YOU HAVE ASK MULTIPLE  QUESTION IN SINGLE REQUEST. SO WE WILL BE ANSWERING ONLY FIRST…

Q: Find the values of a, b, c, d, e, f, g and h such that ax, S(x) = { 6(x – 2)³ + c(x – 2)² + d(x – 2)…

A: GivenS(x)=ax3,0≤x≤2b(x-2)3+c(x-2)2+d(x-2)+e,2≤x≤3f(x-3)3+g(x-3)+h,3≤x≤4such that S(x) is a natural…

Q: find the interval of existence in which the particular solutions of the IVP is vaild

A:

Q: @show that a) G (x,x) => Uu6) Unl) were G is green funcfion

A:

Q: 1. Construct the bisector of XY.

A: We need to draw bisector of line. AS per our guidelines we can not solve multiple questions so I am…

Q: (a) through the midpoint rectangular rule and (b) through the trapezoid rule. Discuss your results…

A:

Q: =: |2| = 1 on closed curve -dz < 2ne, show that inequality exists.

A: Let fz=ez+4z2 Then f has singularity at z=0 of multiplicity 2 Resf;0=limz→0ddzz2×ez+4z2…

Q: 13. Let P be the perimeter of a rectangular fence. Prove that the shape that encloses the maximum…

A:

Q: ☺ show dhat 2) G(x,x) => Uola) Uorlo) were G is green funcfion

A:

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 maximum of 6x? + 17y* on the subset of R? consisting of those points (x, y) such that (x –…

A:

Q: 2) Find divergonce of the following functon Hoy,z) = xe ーZ ーD 472 リ+3yek

A: We will find out the required value.

Q: Prove that for x&gt;0 the inequality 1+2lnx≤x2 is true.

A: Inequality given in the question is: Consider the function; f(x) = 1+2ln(x)-x2 Let us find critical…

Q: Please see attached equation image as I didn't want to enter it incorrectly in this text box

A: Given function is h(x) = f(g(x)) where The function h(x) is given by:

Q: Find the dimensions a and b of the rectangle of the maximal possible area inscribed in a semicircle…

A:

Q: Suppose that the functlons u and w are defined as follows. u (x) =x² +3 w (x) = /x+ 2 Find the…

A:

Q: b. Test that the roots OF Hre folluwing poly nomial sn fis f tht Fent fational root Hicarem P(x) =…

A:

Q: Show that the IVP x" = –6x(x')3, x(-1) = -1, x'(-1) = 1/3, has a unique solution x and find the…

A: The given initial value problem is, x''=-6x(x')3                                     ..............1…

Q: Find the Zero and its order for the funcation fcz) = 1 -Pit z te.

A: We know that, f(z) = (z-z0)n has zero of order n at z=z0, if f(z0)= 0

Q: 4. Show that the intervals S =[1,3] and T =[2,8] are equinumerous by finding a bijection between…

A:

Q: The base of a three-dimensional figure is bound by the graph x = y° on the interv 1, 2]. Vertical…

A: As it is known that the area of an isosceles triangle is given as 12bh where b is the base and h is…

Q: Solve the following inequality graphically in two-dimensional plane:y + 8 ≥ 2x

A: Given:

Q: a) Verify Rolle's Theorem for ƒ(x)= 2.x' – 8.x + 4 over the interval [0,2].

A:

Q: Find x so that the distance between (−4, 3) and (x, 1) is squareroot of 29. (Enter your answers as a…

A: We know that,The distance between two points (x1,y1) and (x2, y2) is given byD= x2-x12+(y2-y1)2

Q: 9) suppose that horx)=1, f,(x)=x ond dz(X) Prove that Ba(f, - where Ba is a Bernyterh Polymomial.

A: Given functions are f0(x)=1, f1(x)=x and f2(x)=x2 Since Bernstein polynomial is…

Q: Show that the class of closed interval [a,b), where a is rational and b is irrationals and a <b, is…

A: Base for topology: A collection B of subsets of topological space X is said to be base for topology…

Q: Glven APQR with vertices P(2, 4), Q(5, 8) and R(9, 5). a. Show that APOR is isosceles b. Show that…

A:

Q: Consider the following points. (-1, 4), (0, 0), (1, 1), (4, 58) (a) Determine the polynomlal…

A: The given points are -1, 4, 0, 0, 1, 1 and 4, 58 We have to determine the polynomial function of…

Q: Find the value of K that make s the funtion fcx) Continus : x*+ 3K メニ2; %3D 2K-X > 2

A:

Q: 8) Find what va lues of x salisfy the fellowing inequality: 3x -1 >2 2x +5

A:

Q: Given the expression |z+3 - 2i = 2, find the geometric region of space where the z exists in. Graph…

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Q: Use the IVT to find an interval of length 0.3 that contains a root of In r = 3 – 2r.

A:

Q: Having aeR and ɛ > 0. Define ɛ-neighborhood of “a"

A: Explanation of the answer is as follows

Q: B. Use indirect proof 1. Show that: Vx€z, if x2- 6x+ 5 is even, then x is odd.

A: Given : x2-6x+5 is even for all x∈ℤ   To prove : x is odd As x2-6x+5 is even . So,  x2-6x+5=2m for…

Q: Consider the following points. (-1, 4), (0, 0), (1, 1), (4, 58) (a) Determine the polynomlal…

A:

Q: Let fa) = x -1E Zs CxJ, wrte fX) as a produt of ireduclble polynomias as Zg.

A: Answer