2. Consider the expansion of ( 2x + =). Assuming k is a positive constant, suppose the term 8. independent of x is 1,451,520. Determine the value of k.

Q: What is the largest root of the polynomial x? + x – 12? О А. 3 В. 4 О с. 1 O D. 2

A: Using factorisation to find roots

Q: 11. Consider the expansion of 3x+ where p> 0. The coefficient of the term in x is equal to the…

A:

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: Let n 2 2. Assume that Fn is prime. show that Fn = -1.

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Q: Find the smallest integer x for which (x4 + 4x)/(x + 2) is O(xx). 01 02

A:

Q: 3. The third term in the expansion of (x +p ) is 252r°. Find the possible values of p. а. +4 с. +2…

A: Given that the third term of the expansion of  (x+p)8 is 252x6. We find all possible values of p.

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Find the 5th term in the expansion of x3 7 2y2) x2

A: The expression is  x3-2y2x27

Q: iid Let X1,, Xn N(u, o). Find 2(n 3) (X2+ + X(n-2)) + 16 X(n-1) +Xn if,E(i) 16 17(n-2) 16(n-3) 4…

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Q: 3. Consider the expansion of (x + 2)°. a. Write the full expansion using the binomial theorem. b.…

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Q: Consider the expansion of (2+x²³²) ¹+¹ ² where 2+2 nt next the coefficient of X² is 1792, Given that…

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Q: 1. 1+ x +x? + x' + x* Find the coefficient of x25 in the expansion of

A: We have to find the coefficient of x25 in the expansion of 11+x+x2+x3+x4.

Q: Use the table below to fill in the missing values. f(z) 2 f(8) - it f(2) -9 then z= Enter an intew…

A: f(8) = 2       If f(x) = 9 then x = 5

Q: Compute the coefficient of xy4 in the expansion of (3x – 4y)7. -

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Find * L(e2t t²)

A: We will use first shifting Theorem to solve this question.

Q: Prove that product notation d/n = nτ(n)/2.

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Q: The Lucas numbers can be generated using the recursive formula: L1 = 2 L2 = 1 LN =LN–1 +LN–2 What is…

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Q: X-H for H, when z = 1.81, x = 33.5, and o = 2. Solve z = (Type an integer or a decimal.)

A: Given , z = 1.81 x  = 33.5 σ = 2 We have to find mean ( μ )

Q: Excercise 1. For small e, find the first two terms in the expansion of each of the roots of P(z,e) =…

A: The given polynomial: For small , Take Substitute value in the given polynomial, This can be…

Q: What is the coefficient of x'y5 in the expansion of (1x + 3y)18? 3,15

A: Use formula of binomial expansion to solve the question.

Q: Suppose W-Exp(5). What is P(W>1)? Round to 4 decimal places.

A: Given that W follows exponential distribution with mean 5.

Q: If g(x) = 5 – x³, find g'(0) and use it to find an equation of the tangent line to the curve y = 5 –…

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

Q: (목+)" Q41. Term independent of x in expansion of is? e 6x3

A: here is the solution

Q: 6. Which polynomials have 4 roots? Select all that apply. 3x* – 81 = 0 4x + 4x + 4 = 0 2x4 + 3x? +…

A: The root of the polynomial is measured by its degree. Degree of a polynomial is the highest power of…

Q: If A= h= - 1 - 20 h 1 1 - 1 21 and |A|=5, find h. Hint: use a co-factor expansion to calculate |A|.

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Q: Prove that r(1/4) r(3/4) = /27. %3D

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Q: Find a positive number x such that the sum of 36x and is as small as possible.

A: We will use basic knowledge of functions, differentiation, and the second term extrema test /…