The Taylor series of x5 - 6x2 + x – 7 at x = 1 is: -8 + 7(x – 1)? + 10(x – 1)³ +5(x – 1)* + (x – 1)5 | the above -11 – 6(x - 1) + 4(x- 1)2 +10(x – 1) + 5(x – 1)* + (x – 1) - - -

Q: (1+x(2)- 2x(2)(1 + x)(2x) (1 +x)*

A: Apply BODMAS rule, to simplify the given expression. First, remove the parenthesis and then…

Q: (a) 5 Find the coefficient of x in the expansion of (2x -) . (b) Hence find the coefficient of x in…

A: You can use the binomial expansion to solve the problems as follows :

Q: 1) (a) Determine the simplest form of the expansion of (2x4 - 1) 4. 4x (b) Determine the coefficient…

A: Consider,(1) (a) Given,(2x4−4x1​)4use the binomial theorem formula to simplify the given…

Q: the expansion of omial theorem to determine the value of the consta 3 < (22²7³. 23 2 (2-3r³y) x…

A: Given expansion is 2-3x8y×2x2y3+3x3-2y219…

Q: (a) (b) Use the quotient-remainder theorem to find the gef{77, 42}. Find ALL integer solutions to…

A: Using quotient remainder theorem we can find the gcf is 7 and all integer solution are q=6n+5 and…

Q: Vx+5 1. State the domain of f(x) = 10° using interval notation.

A: The given equation is

Q: Зх —1 A B (b) (i) Express (1– x)(2 - 3x) in the form - x 2-3x , where A and B are integers. Зх— 1…

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Q: i. Find the coefficient of x in the expansion of ( 2x –÷) . ii. Hence find the coefficient of x in…

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Q: P(x) = 5 x + 13 x5 − 7 x6 − 2 x2     If P is written in descending order, what would be the final…

A: given polynomial is                                               P(x)=5x+13x5-7x6-2x2 P is written…

Q: 1. 2. 3. If the first five terms of the Taylor expansion for f(x) about x = 0 are 5 3 3-7x+ x² +…

A: The given problem is to find the value of f'''(0) and first three terms of taylor series expansion…

Q: What is the rule for this pattern? (figure 1 is 1 block) Of(x)=n+2 Of(x) = 2n Of(x)=n-1 Of(x) = 2n-1

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Q: 13 - What is Taylor polynomial with order 3 generated by f(x) = x° + 3x² + 2x + 4 at x = 1.

A: The Taylor polynomial of order 3 is given as follows :

Q: 3. Determine the 4th term of (3x+ 2y3 6 using The Binomial Theorem.

A: We will find the 4th term

Q: In Z[2√7], show that N(6 + 2√-7) 5 N(1 + 3√-7) but 6 + 2√-7 and 1 + 3√-7 are not associates.

A: As per the question we are given the extended field ℤ [2√-7] and we have to prove that N(6 + 2√-7) =…

Q: 10 [1] Find the coefficient of the term involving x* in the expansion of (3x - a. -262444 b. -262440…

A: We have to find the coefficient of x^4.

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: Compute the constant term in the expansion of (2x³ + ½)¹².

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Q: 8 For which values of mis x - 1 a factor of x³ + m²x² + 3mx + 1? (a) Show that n = 1 is a root of…

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Q: For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6…

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Q: (a) Explicitly check that [7] + [21] = [98] + [–5] in Z13- (b) Find another value of n such that [7]…

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Q: 1. The coefficient of x³y³ in the expansion of (2x + 2y)¹⁰ is 10 2. The constant term in the…

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Q: (c) Find the term independent of x in the expansion of, 15 2 +

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Q: x5 + (2i – 1)x3 - 2ix – 5 a = 5+i

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Q: n Prove that (3i – 2) = ; (3n – 1) for all integers n > 1. - i=1

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Q: 2. (a) Given that (2 + x)" (1-x)" =+ pa³+qx²+7x+s, determine the values of P.4.9, and s. (b) Without…

A: Step 1: Step 2: Step 3: Step 4: