(3)lf R is an integral domain has non zero characteristic, then Char(R)=..... 5 4 9

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: he absolute extrema of J(*) = ,2+2x +9 n(-1,5]. %3D

A: The given function is  f(x)=xx2+2x+9 on [-1,5]

Q: Calculate R3 and L3 for f(x) = x² - 6x + 6 over [1,4].

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Q: 1. (a). Show that (1 · 1) + (0 ∙ 1 + 0) = 1. (b). Find the value of (1 + 1) .

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Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

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Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: 20) √√x(4-x) dx 0 1

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Q: (c) (i) Express the decimal 9.999 in the form where a, b € Z.

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Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: 1. Let f(x) = x² + 1. %3D (a) Compute f(0), f(-1), f(1/2), and f(/2). (b) For what values of x is it…

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Q: 9. Find a calculus-based approximation for V10 – (.92)² –- 2(2.03)².

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Q: nich of the following is a polynomial function? a. y = sin x b. y = cos x C. y = 3x d. y = x³

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Q: 1. What degree are the following polynomials (3.a and 3.b) and monomials (3.c and 3.d)? (a) f(æ) =…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: Q4. Use Newton forward-difference formula and construct appropriate interpolating polynomial and…

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Q: 6. (x – 1

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Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: Evaluate ſ x³ {/ (1 + x³)² dk

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Q: 4. Let f-(x) = g(x) = x-5, k-1(10) + 7 = 10 and h(x) = then find: b. Domain of h(x). c. (hof)(2). (Z…

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Q: Calculate R3 and L3

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Q: 2. Let f: RR by f(x) = -2x + 1. Let A = [2,5] B = [-1,3] C = [−2,3] D = [1, 4]. Find each of the…

A: Here are the solutions:  Note:We have provided the best possible solution for you. Kindly, verify…

Q: Let n be a positive integer. Define the function fn(z) by dzn (2²+2x+2)". Find the value of fn(-1 +…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: Given f(x) = - - 6x + 2, h(x) = 2(x – 6)(x+ 10) and g(x) =(x - 4)²+2 deter write f, g or h) has no…

A: Given,       f(x)=-34x2-6x+2h(x)=2(x-6)(x+10)g(x)=65(x-4)2+2

Q: For what x is x(2x+3) positive?

A: For f(x)=x(ax+b). (1) f(x) is positive: ⇒x(ax+b)>0⇒x>0 and ax+b>0 OR x<0 and…

Q: Ž ( – 1)"x" 1+x

A: Given the power series

Q: -Find Taylor or Maclaurin for the following functions: 4) f (x) = x³ – 2x + 4 at a = 1

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

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Q: dx 1. (x-3)(x-2)

A: Given I=∫1x-3x-2dx To evaluate the integral I:

Q: 2 (x? - х- 6) R (x) X State the domain of the following function : 7(x? + 4 x – 21)

A: Given the function:       Rx=2x2-x-67x2+4x-21 Find the domain of R(x).

Q: 5) Find the velocity of rocket by using Gregory-Newton interpolation polynomial at t=260 sec. time…

A: Let the given table is of the form, where x denotes time(t) and y denotes velocity(v). To find…

Q: 3. What is the degree of the polynomial? * 6x +2-7x* +x' - x O 1 4 O 10 2. O O O

A: Highest power of variable x in polynomial is called degree of polynomial