Obtain the an = $ sum of the series. (sin-—-sinn) W

Q: 2x² + 3x + 3 (x + 1)³ - dx

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Q: 2x-x² dx

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Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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Q: √4x²(x³-5)ª dx = Ox³(x¹² - 25x¹ +250x6 - 1250x³ +6250) + c 12 15 O 16(x³ - 5)4 + c ○(x³ - 5)5 + c…

A: To evaluate ∫4x2x3-54dx Formulae used d(xn)=nxn-1d(constant)=0∫xndx=xn+1n+1+c

Q: Consider the following initial-value problem. f'(x) = 8ex − 4x; f(0) : = 13 Integrate the function…

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Q: Find the vertical asymptotes (if any) of the gr exist, enter DNE.) x³3x² + 4x g(x) = 5x² - 30x + 40

A: g(x) = (1/2x^3-3x^2+4x)/(5x^2-30x+40)  Find the vertical asymptotes?

Q: Using the definition, find the derivative of function 2z-i 1 (z)= at the point z = = -¡. z + 2i

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Q: 3d8 √93

A: Here we have to solve only part d

Q: P1: Calculate the area bounded by the curves: C. y e* and x - 2y + 5 = 0, and y-axis.

A: To calculate the area bounded by the following curves.y=e-x and x-2y+5=0, and y‐axis.

Q: 3 A box with a square base and open top must have a volum of 108000 cm³. We wish to find the…

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Q: Find f(t). ℒ−1{9s / (s - 4)2}

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Q: Find f(t). ℒ−1{(2s + 7) / (s2 + 8s + 65)}

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Q: X xp zo-zXI

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

A: Given :  A piece of cardboard measuring 14 inches by 9 inches is formed into anopen-top box by…

Q: Find all solutions to 2 sin(0) 0 = = - 1 on the interval 0 ≤ 0 < 2π

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Q: 寸

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Q: State the order of the given ordinary differential equation. (1-x)y" - 3xy' + 6y = cos x Determine…

A: Order = highest derivative order = 2

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Concept: Exact differential equation: For the differential equation of the form Mdx+Ndy=0 If ∂M∂y=…

Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A: We have to prove the given equation of complex number

Q: Researchers fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in…

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Q: Solve 2 cos² (x) - 3 cos(x) + 1 = 0 for all solutions 0 ≤ x < 2π X = Give your answers as a list…

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Q: 3.) The natural length of a spring is 8 inches. A force of 20 lb stretches the spring to 10 in. Find…

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Q: P3: Calculate the volume of solid of revolution when the region bounded by y = cos x and x² - y - 2…

A: We have to calculate the volume.

Q: *2t-h 5 if t=2 then h = -1 true O false O

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Q: 2- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = C

A: Given problem:- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = 0

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: Question 13 What is the volume of the solid formed when the region bounded by the curve y=√16x², x =…

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Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

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Q: Which statement describes this graph? 3 15- -10- -5-

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Q: T(n) = (n − 1)!

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Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y c=-2 -3 + (-2, 3).…

A: The graph of the function is  To evaluate: a limx→c+fx, c = -2b limx→c-fx, c = -2c limx→cfx, c = -2

Q: When fully multiplied out, what is the 8th term of (x-3y)¹2?

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Q: A cylindrical tank is full of water. If the radius and height, respective of the tank are 1m and 3m.…

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Q: Determine the critical points of f(x) = er³-2x²-7x Ox=-2 and x = 55393 O There is no critical point.…

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Q: ∫0.00202003x^4/4-0.0185672x^3/3-0.0937054x^2/2+2.17676x+C

A: We have to solve it. But it's not clearly mentioned that, either We have to find integration or…

Q: What is the formula for the nth term of the sequence 5, 8, 11, 14, ...?

A: The given sequence 5, 8, 11, 14,........

Q: If the first-quadrant area bounded by the parabola y = 4 - x² will revolve about the x-axis, the…

A: Given curve, y=4-x2 Portion of given graph rotate around X axis in first quadrant, Therefore Put x=0…

Q: Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents…

A: It

Q: An analysis of the daily output of a factory assembly line shows that about 50t+t²- 1 tunits are…

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Q: Find  f(t). ℒ−1{1/(s - 7)3}

A: The inverse laplace tranform L-11s-73

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

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Q: 3. Let R be the region below bounded by y² + x² = 9 and (y-2)2 + x = 1. (0,3) (a) Set up a (sum of)…

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Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: Aw 2.f(x) 4 3. f (x) = x 9 =

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: Use a graphing utility to graph the equation. Use a standard setting. y = x2 + x − 12   Approximate…

A: The given function y=x2+x-12