Given: In(1+ x) (-1)" xn+1 _if |x| < 1 n + 1 n=0 (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of n=0

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Q: (29.4) Determine whether the series (-1)"-1. n2 + 1 is absolutely convergent, condi- n=1 tionally…

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Q: 5. The subsequence of (xn) = () is.. a) (1층..) 0) (1.층,급.) b) (1,1,1, ..) a) (1.-) 6. The sequence…

A: Every subsequence has a pattern.  According to guidelince we solve only first question.

Q: Find the solution. dy 2y + dx -=x²y²sinx 1 (A) y = х? (sinx - c) B y = x ( sinx +c) y = x²(cosx+c)…

A: We have to find solution of given D. E.

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A: Volume

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Given problem:- Use Lagrange multipliers to find the maximum and minimum values of f subject to the…

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A: Let's find.

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A: According to Newton's law of cooling, we have T(t)=Ts+(T0-Ts)e-ktwhere T(t)- temperature of body at…

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A: Given: I=∫lnxx2dx   As we know the Power rule: ∫xndx=xn+1n+1+C

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Q: 2-4х3 3. lim х--0- 5x2+3x3

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Q: Solve the given third-order differential equation by variation of parameters. y"+ 64y' = sec(8x) |3|…

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A: Scalar Projection of AP on AB is defined as AP→.AB→AB→

Q: 9. Write as a single integral in the form f(x) dx. -1 f(x) dx + f(x) dx - f(x) dx -4 f(x) dx

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Q: whetr he se linea bendent or linea dependent. S - {(-5, -3, 6), (2, -3, 1), (9, 0, 0)} O linearly…

A: To solve the following problem

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Q: S(7(3y +2)(4y + 3y²)³ + sin(3 + 8y))dy

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Q: Evaluate the following integral using the method of partial fraction. (2х3-3х?) dx a. 2x2-7x+5

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: dy +y= y2 sin x

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Q: Find the area of the parallelogram that has u = 2i – j+ 2k and v = 2j + 3k as adjacent sides. NOTE:…

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Q: Instructions: (I) Use Limit Laws to find the limit of each given problem. (II) You may only use…

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Q: Find: e sinx dx tanx CsC x dx 4x3 + 4x²+ x

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Q: Referring to the graph above, which of the following statements is correct: 1. f″(x) 0 for all x

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Q: u = 5i + 4j, v= 3i + 2j (a) Find the projection of u onto v. (b) Find the vector component of u…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z² (2,…

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: Solution of question is written in below steps.

Q: Show that the lines L1 : x = 4 – t, y= 2t, z = 5+t and L2 : x = 1+4t, y= 3 – 8t, z= 5 – 4t are…

A: Let's find.

Q: Consider the points A(3, –3, 2), B(4,–5,0), C(-1, –4,0), and D(6, 2, –3). (a) Find the volume of the…

A: AB→ = i -2j-2kAC→ = -4i-j-2kAD→ = 3i+5j-5k Volume of parallelepiped with AB→, AC→ ,AD→ as adjacent…

Q: Solve the following differential equations using the method of undetermined coefficients. y" – 2y" +…

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Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) sin(4h) lim h h→0

A: The given limit,      limh→0sin4hh

Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

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Q: The term t (in years) of a $200,000 home mortgage at 7.5% interest can be approximated by the…

A: Given that the term t of a $200,000 home mortgage at 7.5% interest can be approximated by the…

Q: Use a computer algebra system to graph fand to find f' and f". Use graphs of these derivatives to…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: Vx* Show that for x > 1, coshx-(cosh 3x- sinh? 3r dx 3x) In(x+ Vx² (b) )= In(x+ Vx .2 +Vx -1

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Q: Determine if the following statement is true or false. The points P1(12, 9, 7), P2(6, 4, 0), P3(0, –…

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Q: (30.4) Apply the ratio or root test and state whether the series is convergent (2n)! n=1 or…

A: Given:     series ∑n=1∞12n!     Split the series:     =∑n=0∞12n!+∑n=00-12n! Since the bounds are…

Q: 4. CHOOSE one of the following functions (CIRCLE YOUR CHOICE): y = 2 log(x + 3) – 5 Asymptote(s)…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: We are given a function  f(x) = e-x sin(x) -e7x cos(x)  We have to find a linear differential…