Q.2\Prove the Maclaurin series: (-1)"-1xn In(1+ x) = En=1' ,-1

Q: ) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the finit...

A: Area under the curve =∫ab(upper curve -lower curve)dx  

Q: 4k? – 2k + 6 8k7 + k – 8 O The series converges. O The series diverges.

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Q: sinx dx TI cosx t ecoSX 2

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Q: Given the following trigonometric values, find the angles ? within the interval 0 ≤ ? ≤ 2? that sati...

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Q: dx (c) x² /4 – x2

A: Please see the below picture for detailed solution. 

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 2(-1)*+1_k+ 10...

A:   ak =(-1)k+1 k+10k(k+11) {bk} =k+10k(k+11)bk - bk+1 =k+10k(k+11)-k+11(k+1)(k+12)=k3+23k2+142k+120-k...

Q: Q2) A) Graph the curve Y = x (x +5)(x -3) between the value of x [-5, 3], then find the area of the ...

A: area under the curve

Q: Find the derivative of the function. Q(x) = V ex + x Q'(x) = %3D

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Q: solve the given ini tial -value problem dx -x = gyz , x(6)=1 dy 2. X (y). %3D Give the largest inter...

A: linear differential equation

Q: Find the maximum or minimum value of the quadratic function g(x) = 2x² + 6x + 3.

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Q: Solve the given differential equation by separation of variables. xy + 7x - y - 7 xy - 2x + 8y - 16 ...

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Q: (e) /a (с) dx e2x 2.х

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Q: dy ay +b who dt Write down a differential equation of the form solutions all approach y 3 as t → 4 3...

A: We will find the Differential equation. 

Q: Use the formula for the binomial series: (1 + x)" 1 + mx + m(m-1)2 m(m-1)..(m-k+1), + + ... ... 2! k...

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Q: dx 3. S XVx-1

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Q: ) de 1 cos330 cos830. sin³30

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Q: The derivative of the function 3+ln x is: y = cos(In x)

A: y=3+ln(x)cos(ln(x)Differentiate w.r.t.xApply the Quotient Rule:  fg'=f '·g-g'·fg2dydx=ddx3+lnxcoslnx...

Q: Given: Sum of the points of the ellipse from foci = 30 Foci: (2,1) (10,1) c = 4 a=? b=? Center: ...

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Q: X+イ (X+6x+3)

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Q: Question 1 The domain of the following function f(x.v) = In(x-v+1) is given by the equation:

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Q: Compute the multiplicative inverses of the following (if they exist) usin Using the Euclidean algori...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: Find the radius of convergence and the interval of convergence. k(k + 5) k=1 Radius of convergence: ...

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Limit comparison Test : Suppose ∑ak and ∑bk be two positive term series and        L =limk→∞|akbk| I...

Q: A wooden artifact from an ancient tomb contains 50 percent of the carbon-14 that is present in livin...

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Q: Find the indefinite integral. (Use C for the constant of integration. 9. de cos(8) – 1

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Q: 12x Ja +9)6 dx

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Q: Solve the given initial-value problem. The DE is a Bernoulli equation. y1/2 dy + y3/2 = 1, y(0) = 16...

A: differential equation

Q: (sin y – y sin x) dx + (cos x + x cos y – y) dy = 0

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Q: Express the given quantity in terms of sin x and cos x. Sin (2n – x)

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Q: sin 4x Given: - Txwhat is the appropriate formula to find the integral? cos?(4x) (2 – 3 sec 4x) 1 (A...

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Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about x = x0 and then find the nth Taylor...

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Q: Verify that the indicated function is an explicit solution of the given differential equation. Assum...

A: Given:     y''-6y'+25y=0     y=e3xcos4x      y'=ddxe3xcos4x  Apply the product rule: ux·vx'=u'x·vx+u...

Q: 4. Using the graphing strategy discussed in class, sketch a graph of the function 1 f (x) = (x – 4)/...

A: 4. Using the graphing strategy discussed in class, sketch a graph of the function f(x) = (x − 4) 9/5...

Q: an experiment in which a coin is tossed thrice. Let X be the number of heads. Find the mean, varianc...

A: We will find mean, variance and standard deviation

Q: (0) E sin ) sin 2(n+ 1) - n=1

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Q: sin 0 d0 cos? 0 +5 cos 0 +6

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Q: Consider the integral dx . Using u-substitution, what is an appropriate u and du? 2e -2x A u=/3 e2*....

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Q: (a) If f(x) = V3 – x, find the inverse function f. %3D

A: Topic = Functions

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: An+1 to determine if the sequence { ne" } is strictly increasing or strictly decreasing. an Use the ...

A: By see this solution in below

Q: Problem 2: Choose Group 4 show complete solutions based from second pic.:)))

A: Please see the below picture for detailed solution. 

Q: . Given the point Q(1,-2,4) and a plane p: 3x + 2y + 6z = 5, find a) The distance from Q to p. b) Th...

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Q: 2csct -1 D csct +2

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Q: 2 2 x+y e to pday dyd x |-X

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Q: 12X dx (x+9)0

A: We know, ∫xndx= x(n+1)/(n+1) Let I= ∫12x/(x+9)⁶ dx

Q: Determine whether the alternating series converges. 6ln k 1)* k k= 3 O The series diverges. The seri...

A: The given series is summation of (-1)k6lnk/k , k from 3 to infinity.

Q: Fill in the table with the correct information by referring to the function f below. The table conta...

A: We will check at each point of interval to determine the continuity or discontinuity.

Q: Determine whether the series converges. 1 Σ k + 10 k=1 The series eTextbo converges diverges

A: To determine whether the series converges.∑k=1∞ 1k+10

Q: rve Y= x (x+5)(x-3) between the va rea of the finite region bounded by ven quantity in terms of sin ...

A: We have to find the following given conditions according to the given information

Q: sec Hovy long it will tace the bor te ach 99°C I Round the ani wer to one deaimal place ] Tsec

A: