Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) 1 Σ (-1) 72n+1(2n + 1) n=0

Q: If 0 = 1TT 4

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Q: Find the indefinite integral. (Use C for the constant of integration.) J In(sec (50)|) + C tan 50 de

A: Given integral ∫tan5θdθ = ? As we know that tanθ = sinθcosθ

Q: Find the indefinite integral. (Use C for the constant of integration.) e2x 9 + e4x garctan 3 dx +C

A: ∫e2x9+e4xdx Apply u substitution Let  u=e2x & dudx=2e2x ⇒du=e2x2dx…

Q: 7xy lim (z,y) → (0,0) x2 + y² 11

A: Here we need to find the limit for the function

Q: ce the following integrals: 3√arctan x 1+x² dx

A: To solve the following

Q: At one point in an artery the velocity of blood is 5 cm/s and the diameter is 0.33 cm. If the…

A: At one point: Velocity, v1=5cm/s. Diameter, d1=0.33cm. At another point: Velocity, v1=10cm/s.…

Q: Find the area of the region. 4 V X y = y 10 4 3 2 1 2 3 4 5 6 7 8 9 101112131415161718 X

A: The function is given by y = 4x The raph of the function is To determine: The area of the shaded…

Q: use a test of convergence to determine if the follow series converges or diverges: summation where…

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Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) 5xªy…

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Q: The demand function for a certain bran of CD is given by = -0.01x² - 0.1x + 37 p=

A: The  demand  function for a  certain  brand of CD is given  by p = -0.01x² -0.1x + 37  where p is…

Q: Suppose an arrow is shot upward on the moon with a velocity of 51 meters per second, then its…

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Q: (a) Sketch y = secx on a restricted domain of length 7 where the function is one-to- one. Choose…

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Q: 12y 10. Section 7.7 Evaluate: [[(x² - 4y)dxdy -10

A: ∫-11∫02yx2-4ydxdy

Q: 19. MJ Corp has a store in the Park Green Center (PGC). The PGC has 4 stores. MJ Corp is in store 1,…

A: MJ Corp has a store in the Park Green Center (PGC). The PGC has 4 stores. MJ Corp is in store 1,…

Q: Rate oil is pumped out (millions of barrels/month) -Select- Select- 40 35 30 Use the graph of r(t)…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Problem 4. Find the area of the surface of revolution generated by revolving the plane curve y=2 x…

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Q: Use the graph to find each limit. graph of f(x) -5 -4 الا -3 + -2 5 1 -5 A 2 3 4

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Q: Convert the point (p, 0, 6) = 5, 2π, 3T 3³7) to 4 to Cartesian coordinates. Give answers either as…

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Q: Find the moments of inertia I, I, Io for the lamina below. Ix Iy Io II II || D is bounded by y = ex,…

A: The given Lamina is: D=y=ex,  y=0,  x=0  and  x=1ρ(x, y)=17y

Q: Use the quotient rule to find the derivative of 4x² + 2 k(x) 6x - 2 =

A: We know that the quotient rules of the d/dx(u/v)=(v*du/dx-u*dv/dx)/v^2

Q: 31. (a) Sketch an accurate graph of the cosine on the domain (-27, 27). Use this to sketch an…

A: We have to draw the graphs of the following

Q: find the magnitude and direction angle of the following vector, write your angle in degrees rounded…

A: Given: u = -13i - 8j We are required to find: Magnitude of vector u=||u||=?Direction angle of vector…

Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

A: The left Riemann sum∫abf(x)dx≈∆x(f(x0)+f(x1)+f(x2)+⋯+f(xn-2)+f(xn-1))∆x=b-an

Q: 8. A dog chases a squirrel at a rate of 3 m/s. The squirrel dashes up a tree trunk (vertical) at the…

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Q: Suppose F(x, y) = (2x – 4y)i + 3xj and C is the counter-clockwise oriented sector of a circle…

A: Given function (2x - 4y)i  + 3xj

Q: 10. Find lim n→∞ n-3 n+3 4n

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Q: Suppose a product's cost function is given by 8q² + 1000q, where C(q) is in C(q) dollars and q is…

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Q: 12. (From 7.3) Find any relative extrema or saddlepoints for f(x,y) = 12xy-x³-6y² Note D= fxx fyy -…

A: For the given note , we will find relative extreme or saddle points .

Q: b) x-8 and the 10th term is p² x18 The 5th term of a geometric series is where p > 0. i. Find the…

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Q: Sketch the curve and find the area that it encloses. r=2+2cos(theta)

A: r=2+2cosθ

Q: 2. Evaluate the integral. [x³√√x² +1dx

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Q: 1) Find the area of the triangle P(-2, -6, -1), Q (-2,-4, 1), R(3,6,6)

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Q: Consider the vector field F(x, y, z) = (6y, 6x, −z). Show that F is a gradient vector field F = VV…

A: The given vector field is:F(x, y, z)=6y, 6x, -z

Q: 1. Sketch a graph of a function f that is differentiable and that satisfies the following…

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Q: Find a potential function for F. 4x, 1-2 +1-2x² {(x,y): y>0} F=i+ y *** A general expression for the…

A: The given vector field is: F=4xyi+1-2x2y2j          x, y: y>0

Q: Speedometer readings for a vehicle (in motion) at 6-second intervals are given in the table.

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Q: 8. Section 7.6 a. Use the differential df to estimate the change in f(x,y) when x changes from 1 to…

A: We have given a function f(x,y) = x2y + 2xy3

Q: Let ƒ(x) = (3 – 2x)6 - f(x) has one critical value at A = For x A, f(x) is [Select an answer ✓

A: fx=3-2x6

Q: The derivative of f(x) = 18xe is-18xe (Type an exact answer in terms of e.) +18e

A: We know that the product rules of the derivative d/dx(uv)=u*dv/dx+v*du

Q: 100x² The dose-response for a specific drug is f(x) = x² +0.08' from a dose of a grams of a drug,…

A: Given dose-response function for a specific drug is f(x)=100x2x2+0.08, 0≤x≤1.5, x is in grams.

Q: 10. Find the Taylor polynomials P3 and P4 centered at a = 0 for f(x) = (1 + x) −³.

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Q: a. Find the Jacobian of the transformation x = 2u, y = 4uv and sketch the region G: 2 ≤2u≤ 4, 4 ≤…

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Q: Find the mass and center of mass of the solid E with the given density p. E is the cube 0 ≤ x ≤ a, 0…

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Q: 1. Evaluate the integral using substitution. TC/3 π/6 cos*x sin x dx

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Q: Find a potential function f for the field F = 5y + 32 (2 1 + 10x j+ 6x k). A general expression for…

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Q: Find a parametric equation of a line that passes through the point (1,3,-4) and is perpendicular to…

A: To find a parametric equation of a line that passes through the point 1, 3, -4 and is perpendicular…

Q: 47. fin "In (ln x)ln xdx X

A: To find out the integration.

Q: Evaluate the double integral. J бу 4x5 +1 dA, D = {(x, y) | 0 ≤ x ≤ 1,0 ≤ y ≤ x²=

A: ∬D6y4x5+1dA, D=x,y:0≤x≤1,0≤y≤x2

Q: . Find the constants a and b such that the function 6, x 5-1 f(x)= ax+b,-13 is continuous on the…

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Q: A radioactive substance decays according to the following function, where y0 is the initial amount…

A: A radioactive substance decays according to the following function. y=y0·e-0.0741t where, y0 is the…