Find the coefficient of x16 in (x + x²+x³ +x4 + x³)(x² +x³ +xª + · . .)5.

Q: . What is the coefficient of a" in (2 – x)"?

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Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

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Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

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Q: (4b) Prove that there exists no positive integer x such that 2x < x² < 3x.

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Q: Use the elimination method to find all soluti { % 4x - Зу 3-24 -7x + 6y = { By = 45

A: Given,             The system of equations are                4x-3y=-24                -7x+6y=45

Q: 9. For |x|<1, prove that 8x 16x 24x 1-x1+x 1-x 2 8x 8x = 1+ (1 – x)? (1+x2 (1-x)? ...

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Q: Show that x19 + x8+ 1 has multiple zeros in some extension of Z3.

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Q: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: Given is a expression  1215-x&gt;24-2x2. It is required to prove the given expression for all…

Q: Prove that there exists at least one solution to the equation 4x+ 3x +1 = 4x2.

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Q: Find all solutions of x2 - x + 2 = 0 over Z3[i].

A: Given: Z3i=a+bi|a,b∈Z3       =0, 1, 2, i, 1+i, 2+i, 2i, 1+2i, 2+2i We have to find all solutions for…

Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

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Q: 18x- 2(3x + 1) = 5x – 16; Prove: x = -2 %3D

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Q: Prove that f (x) = x3 + 3x2 + 6x has precisely one real root.

A: Number of real zeros of a quadratic equation can be determined using its discriminant. For a…

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: Find the 4 - x' -x²(4 – x²) = 2 i5 (4 - x*) + C 3 x²(4 – x²) 5 3 15

A: Please see the solutions below.

Q: 9. Find the general solutions of X' = AX with A =

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Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: 3. Find the coefficient of xy' in (2x + 3y)°.

A: The provided information is we find the coefficient of  x2y7    in (2x+3y)9 Then, (79)*(2x)2*(3y)7…

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: prove using the IVT. 2x + 3x = 4x has a solution.

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Q: Prove that x2 + 3x + 3 ≥ 0 for all x.

A: We have been given the quadratic equation  x2+3x+3

Q: what is the characteristic of Z6xZ9

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Q: 7.Find a²z of z = 2x³-5xy² xy

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Q: et) of a ball thrown by a child is 1 -x² + 6x + 3 14 -

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Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: Prove that ax² bx C + + (x − a) (x −b) (x −c) (x-b) (x-c) x-c -+1 x³ 3 (x-a)(x-b)(x-c)

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Q: If y3-3ax2+x3=0,then prove that y2+2a2x2y-5=0

A: Solution of this question is

Q: (a) Show that (x2 + v2x + 1)(x² – v2x + 1) = x* + 1.

A: Given that: (x2+2x+1)(x2-2x+1)   NOTE: As per our answering guidelines, we can only answer 1…

Q: Find the term of (x + +)° that does not contain x.

A: Given expression is, x+1x6. The general term is given by, Cknakbn-k. In the given expression,…

Q: Prove that x -2x+2>0 for value of x.

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Q: A³ f2 = V³ fs 3

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Q: Show that (z3 z4) -1 = (z3-1. z4-1)

A: We prove the given statement by taking Z3=x3+iy3, and Z4=x4+iy4. After using the fact of…

Q: Prove that ∇2y8 = y8 − 2y7 + y6.

A: We have ∇yn=yn-yn-1    where ∇ is backward difference operator.

Q: Suppose that X is a (A = e-100, p = 3e-100)-BCP. %3D What is P(X(1)X (2)X(3) = 4)?

A: Correct answer is 4.

Q: (2) Determine k such kx² – 4x +- = 0 that has real and different solutions.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find the critical number of f(x) = 3x^2 - 18x + 4

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Q: Use Giramer Rule to Find ,z -2x + 33-Z = 1 メ+29-2-4 -2x -+7 = -3

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Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

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Q: Prove that x3 x7

A: we have to prove

Q: +prove by indirect method that i X+y >5 then or y>3. x>2

A: We need to prove that if x+y&gt;5 then x&gt;2 or y&gt;3

Q: Find critical number of g(x) = x^2 - 8x +9

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Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Q: 3.) Find the der ivative of cosCx) (5x+) 니 (5x+1)

A: Given :           cosx1x25x+14

Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33

Q: 29. For |x|<1, prove that 16x 24x 8x 1 + 1-x1+x 1-x ..... .. 8x 8x = 1+ (1- x)? (1+x)²' (1-x)?

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Q: 4. Prove that f(r) = 4x³ - 8² + 2x + 1 has three real zeros. %3D

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