Show that the length of the nth interval in the bisection method satisfies b-a bn-an 2"-1*

Q: why is 1t that the error term Rn(x) Is Finitely bounded In every Taylor polynomia? Also why is…

A: theory:

Q: Use integral tables to evaluate the integral. S- 1 xp. xV64 - x2

A: Evaluate the given integral  ∫1x64-x2dx by using table of integrals as we know that from the table…

Q: Use four iterations of Bisection to estimate the root of In (r) = 0.70 on the interval (0.50, 2).…

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Q: OShow that in 27 and use Soot method has bisection approximation to the Soot * at leest within a the…

A: The given equation is. fx=x3+4x2-10=0 fx=x3+4x2-10 To find the root in the interval 1,2 that is…

Q: The interval [1, 5] is divided into eight subintervals. (a) What is the left endpoint of the last…

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Q: Compute the indicated left or right sum for the given functioi ntèrval. 1 L4 for f(x) = on [2,4] %3D

A: We are asked to find the right sum of the integral.

Q: If the interval [4, 18] is partitioned into n = 28 subintervals of equal length, what is Δx?

A: Total length of [4,18] is (18-4)=14  Given that, n= number of partitions= 28

Q: 2. Use a lincar approximation to estimate /9.3.

A: In this question we have to use a linear approximation to estimate 9.3.

Q: Find the Riemann sum of f(x)=square root of x on [4,9] with 4 subintervals and right endpoints.…

A: To find the Riemann sum using right endpoints

Q: Graph the integrand and use geometry to evaluate the integral. V36-x2 đx O 36 O 36 O 18

A: We will solve the problem

Q: 2. Expand (1-x) in ascending powers of x until the term in x'. By using x= - find the 40…

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Q: Evaluate the integral: */64 – a°dz .3 2 -

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Q: Use the Remainder Estimation Theorem to find an interval containing x = 0 throughout which f(x) =…

A: Given f(x)=cosx, which is approximated by the polynomial p(x) = 1−(x²/2!). We need to use Remainder…

Q: evaluate the integral using the methods covered in the text so far.

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Q: Expand in ascending powers of x up to and including the term in x. 7x assuming x = 25 estimate v13…

A: Given: 1+x1-7x12

Q: Use DeMoirve's Theorem to find: (1– iv3)2

A: We first try to express 1-i3 using polar form.r=12+(-3)2=1+3=4=2θ=tan-1yx=tan-1-31=tan-1-3=-π3So,…

Q: Q1/is the funection fex)- dferentimble at X=-\

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Q: Find the positive root in 4th iteration of the equation xeX-3 in the interval [1,2] using Regula…

A: We have to find the positive root in the 4th iteration of the given equation in the interval 1,2…

Q: (x – 2)? – In x = 0, [1,2]

A: Sol

Q: A 6x 6 square is tiled by 2x 1 dominoes. Prove that it has at least one fault-line, that is, a…

A: Consider a 6×6 square which is tiled by 2×1 dominoes. Suppose the 6×6 square has no fault lines.…

Q: Evaluate (x2 – 2x³) dx using the limit of Riemann sums.

A: given integration is                                       I=∫01x2-2x3dx we have to find value of…

Q: Evaluate using cauchy's Residue Evaliate theorem.

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Q: By Find the Taylor senies for fixl= sm x Compating deriratives, at x=0.

A: We know that, Taylor series for fx=sinx at x=a can be found as Now, The Taylor series around a=0 is…

Q: a) Determine the number M and the interval width h so that the Composite Simpson Rule for 2M…

A: The formula for the composite Simpson's rule is . The error in the composite Simpson's rule can be…

Q: Prove that, among all rectangles with a fixed perimeter a square has the largest area.

A: 1) Let the length of the rectangle be l. Let the breadth of the rectangle be b. Perimeter of the…

Q: Find the integral of funcdss7 x/Snca) when ns6,7 and the intereil (15) (Gmpare the esults) by Simp…

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Q: If ø + SCR is bounded above, then .S has a supremum إختر واحداً: ibs

A: I have proved by contradiction

Q: Use the method of, logant to differentiate the fune tion thoms d fferentiation Do not use any other…

A: The solution are next step

Q: 1. Use the Intermediate Value Theorem to nd an interval of length one that contains a root of f(x)…

A: According to Intermediate Value theorem,Any continuous function f has a solution in the interval…

Q: - Prove thas the scries 2+x2 3+X2 4+x niformcy conuergen2 in any interval?

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Q: Compute the area under f(x) = 3x7 – 2 over the interval x = 4 to x = 16. -

A: We will find out the required area.

Q: Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.

A: As per the information, we will first find a recurrence relationship of the sequence, then find its…

Q: Prove that, cosh-'x = In |x + vx² – 1 for x 2 1 -기/

A: This question is based on Cosine hyperbola.

Q: Find 2 pOsitive real numbers x and y such that their s um is 40 and their product is as large as…

A: SOLUTION-

Q: Evaluate the integral: 36 - а2 -de 4x2

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Q: Suppose we use a 6-th degree polynom, PeW to estimete gox) = 2e* with data points (Xi,9(X;)) where…

A: As per Bartleby's answering policy, we can answer only one question. So kindly post the remaining…

Q: it is unbaised estimated of a Then Show That ta is baised estimated of 02. Theorem:- if

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Q: Find the residue of - (:- 1)* at its pole

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Q: Use Taylor senes to wrik Hhe at 2 For a machine Fad

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The integral x²/4 - x²dx can be determined using the substitution 4- x2 = t.

A: Given integral: ∫02x24-x2dx

Q: NIIVISIDIE D 4. Prove that v3 is not rational. 5 Provo

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Q: Calculate the definite integral goven belaw 2 3x- 3 x2 - 2x + 6 -2

A: Using substitution method

Q: 8. S(1- sec3x)²dx

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Q: Use trapezoidal rule to approximate the integral f√3+2x³dx; n = 6 O 11.50676706 O 11.20676706 O…

A: An integral is given. The objective is to approximate it using trapezoidal rule. According to…

Q: So I need to keep the 4 and the cubed in the integral??

A: Yes, you have missed the "4" and the cube.

Q: The term r ryis homogenous of degree two. -

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Q: section method to

A: Given,         f(x)=x-cos(x);     0, π

Q: If fel²() and gelices. prove that fgeles.

A: Given that f∈L2(u), g∈L2(u) By definition If  g∈L2(u)⇒||g||L2&lt;∞

Q: Find the polynomianl degree 9 centered at 0 that best approxixmates f(x)= f(x)=1/ 7sqrt(1+x^3) Now…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.