Find the fifth term in the expansion of (x3 + √y)13.

Q: In the expansion of 5x + the value of the constant term is

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Q: -3t 712e Sinzt 37-47=

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Q: What is the value of f(2) for the polynomial x ^ 3 + 3x ^ 2 - x + 1 ? What does this mean about the…

A: Here, fx=x3+3x2-x+1

Q: Find the fourth term of (2x - 5y)4 without fully expanding the binomial.

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Q: What is the coefficient of xy³ when (2y-x)° is expanded by the binomial theorem?

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Q: Evaluate integral the 6x ..d. (x²+4)(2x-2)

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Q: 2. Let h(x) = |9 – x²].

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Q: Find f-l (n) for 8ln) = n2-6n and its %3D domarn

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Q: Find the fourth term in the expansion of (3x + 2y)7.

A: the given expression is (3x+2y)7.

Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

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

A: The expression is  x3-2y2x27

Q: What is the coefficient of the term containing x^7y in the expansion of (3x + y)^8?

A: Topic = Algebra

Q: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

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Q: Find the term indicated in the expansion: (x + 2y)10; the term containing y6

A: we have to find the term indicated in the expansion: (x + 2y)10; the term containing y6

Q: Find the second order derivation for y = e-3x².

A: d2dx2e-3x2

Q: Find the coefficient of the term xy in the expansion of (2x3-y)5.

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

A: We will find the 4th term

Q: Find the Taylor polynomials p3 and p4 centered at a = 1 for ƒ(x) = 8√x.

A: Given f(x)=8x centered at a=1

Q: b) Used bisection method to find the root of f(x)= x³ + 3x-5, Do calculation until six iterations in…

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Q: Find the coefficient of at in the product (1 + 2a)* (2 – a) using binomial

A: Introduction :

Q: Find the constant C such that .4 x3 - 3x + 5 < C,

A: x3 - 3 x + 5≤c x∈{0,3}

Q: Find the fifth term in the expansion of (2x + y)9.

A: We can use the binomial expansion formula to find the fifth term of the given expression. We have…

Q: Find the term indicated in the expansion (x + 2y)10; the term containing y6.

A: The given expression is x+2y10 To find term containing y6

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: The average pollen count in a certain city on day x of the pollen season is P(x)=8x − 0.2x2 (for 0…

A: Consider the given function,  Represent the pollen count in a city on the day.   The day, which the…

Q: What is the coefficient of x5y7 in the expansion of (x+y)12?

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Q: What is the coefficient of the term containing x^2*y^3 in the expansion of (2x-3y)^5?

A: In order to find the coefficient use binomial theorem, which is given below.

Q: Find all n EN for which is the polynomial x2n + x" +1 divisible by (x)f g(x) = x² + x + 1?

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Q: Determine the coefficient of the x'y term in the expansion of (2a + 3y) 2.

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Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - cis a factor of…

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Q: x² + 6x – 1

A: We have to express  x2+6x-1 in the form (x-m)2+n.

Q: Which term in the expansion of 2x is a constant?

A: 12x3-x58

Q: find the coefficient of t8 in expansion of 2t(3+t)20

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Q: Determine the upper bound on the error in the approximation – 16x5 + 256x° if |x| < 0.2 - 1+16x4

A: Given:x1+16x4 ≈x-16x5 + 256x9

Q: If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?

A: The given function is: f(x)=2x3+Ax2+4x-5

Q: Find the Taylor polynomials p3 and p4 centered at a = 1 for f(x) = 8/x

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Q: x2 + 4x + 13 12

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Q: What is the coefficient of the term containing x^3y in the expansion of (5x+y)^4?

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Q: Find the constant term in the expansion of (2x + 1/x^3)^8

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Q: 12x 3 3 15 12 x4

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Q: Find the coefficient of x°y° in the expansion of (2x – y)³. -

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Q: Find the fifth Taylor polynomial of x3 - 7x2 + 8 at x = 0.

A: Given: fx=x3-7x2+8

Q: What is the coefficient of the term containing x^2y in the expansion of (4x+y)^3?

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Q: fx)=xex,n+4

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Q: Find the third Taylor polynomial for f(x)= cubed root of x centered at 8

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

A: Given :           cosx1x25x+14

Q: Which term in the expansion of 1 3 2x I is a constant?

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Q: 3s Use the convolution theorem to find L-1{

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