Determine whether the series converges, and if so find its sum. If the series diverges, indicate that using the checkbox. NOTE: Enter the exact answer as improper fraction if necessary. Σ(3) k+2 = The series diverges.

Q: x² + y² = 8 y = x + 4

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Q: 3. A semi-sphere tank of radius 7 m is full of water. How much work is needed to pump all of the…

A: Water tank radius= 7m  Water density = 1000km/m3  Find the work required to pump out the water .

Q: 11. \mbox{If a particle's velocity is given by)\:v(t)--t+2\:\mbox (and its) distance at 1-2 is…

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Q: Determine whether the following function is a solution to the differential equation. y = ₁x + ₂x³ +…

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Q: Determine the solution for the following differential equation. Check first if the equation is an…

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Q: Let N. H. S. D. R. J. and B be the propositions: N: Mr. Smith is the brakeman's next-door neighbor…

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Q: A particle is moving along a curve such that its speed at time t is (x (1), y(t)), where x (t)- and…

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Q: show that the lim DNE. In (x4 + 2y² 1) e + y² - 2 lim (x,y) → (0,1) 2x²

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Q: 11. g(x) = X, x-1, x < 0 x ≥0

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Q: Find solution y(t) to the initial value problem: ty^2y'=2y^3+t^3, y(1)=5, t>=1

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Q: 1 + 1 = 3 if and only if 2 + 2 = 3. True or false? If 1 < 0, then 3 = 4. True or false?

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Q: Suppose z = f(u, v), where f(u, v), fu(u, v) and f(u, v) are differentiable functions of u and v.…

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Q: Problem 2: Using index notation, demonstrate mathematically the following equations: 1- uxv=-vxu 2-…

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Q: 1. Using differentials, solve for the approximate change in the hypotenuse of a right triangle if…

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Q: 3. Determine whether the following function y = c₂x + c₂x³ + 2x²e² is a solution to the differential…

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Q: Consider the following function. Find the following values. X→-1 lim f(x) X→-1 f(-1) = f(1) f(x) =…

A: See this solution in below.

Q: B. Given Determine if the DE is DE is EXACT (4x³y - 18x²2 ty) dx + (x4 + 3y² + x) dy = 0, y(1) = -2

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Q: 28. Write the component form of the vector of length 5 that makes an angle of 30 degrees with the x…

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Q: 2. Let f(x) = cx² + 7. If f(-2) = 13, find c.

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Q: A company produces very unusual CD's for which the variable cost is $20 per CD and the fixed costs…

A: Concept: For break even the profit is zero P(x)=0 Also the formula used to find the value of…

Q: x² + y² = 8 y = x + 4

A: Solution

Q: 34. t-36 f(-) dx = -36, which of the following must Given that be true? A. 6-36f (p) dp = -36 B. −…

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Q: If S = {a, b, c} with P(a) = 4P(b) = 3P(c), find P(a).

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Q: ermine lim -1- 2x³5x2 x² - 1

A: Given query is to find the limit of the expression.

Q: The following function expresses an income tax that is 20% for incomes below $5000, and otherwise is…

A: Given  F(x) = .20x when  0&lt;x&gt;5000 ...............1 F(x)=1000 + 0.30(x-5000) when…

Q: (a) Evaluate 3x² + 2y² lim (x,y) →(0,0) √√x² + y² (b) In (3-4)

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Q: (2xy — sin x)dx + (x² − cos y)dy = 0 -

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Q: Enter the exact answers. (a) Find the average rate of change of y = rave = with respect to x over…

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Q: Using differentials, solve for the approximate change in the hypotenuse of a right triangle if the…

A: Let l1,l2 be the legs of this triangle and h be the hypotenuse. Then from Pythagoras theorem we…

Q: Compute the second-order partial derivatives of f(x, y) = e5x² - 4у2 a² f дх2 -(x, y) 22 f дхду 22 f…

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Q: 9. y(cos³x) (cos²2y)

A: We are asked to find the solution of the differential equation

Q: A loan shark lends you $90 at 2% compound interest per week (this is a weekly, not an annual rate).…

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Q: 15. Determine the particular solution of the following differential Where: x=0; y=1 Provide your own…

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Q: Set up the definite integral required to find the area of the region between the graph of y=x²-15…

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Q: 20. If you use the ratio test on the divergent series $ Σ2-1 =1 inequalities will result? n+4 A.…

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Q: Write an equation for line L in point-slope form and slope-intercept form. L is perpendicular to y =…

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Q: A television camera at ground level is filming the lift-off of a space shuttle at a point 750 meters…

A: As we know that cosθ=BaseHypotenus for a right angle triangle.

Q: If the area between the curve is 36 units. Find the value of c. 4 f(x)=x²-c C

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Q: Starting with 2 = A + B₁ show that 2 x 2 = 0 ledd's to A×B = - B × A

A: Given query is to find prove above vector operation.

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

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Q: ye-cosx dx — 3 tan x dx +tan x (e-cosx) dy = 0

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Q: Solve the DE y' = xe2y, subject to the initial condition y(0) = -1. Oy = -(1/2) In (-x^2 - e^2) Oy =…

A: This differential equation can be solved by using the method of separation of variables.

Q: Differentiate the function: F(t)= (6x-5)2

A: Differentiate the function: F(t)= (6x-5)2

Q: Find the solution of each of the following initial value problems. y(0) = 1 (a) y' - y = 2te²t, (b)…

A: As you have asked to solve part a only so I am doing only that one. a. Given differential equation,…

Q: da (cos x tan z) =

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Q: Show that f(x, y) = ln(eax + ey) satisfies fx(x, y) + fy(x, y) = a.

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Q: Find the average rate of change of the function f(x) = 3x from x₁ = 0 to X₂ = 7. The average rate of…

A: Topic = Function

Q: Evaluate [ cos²x = 2

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Q: J 3x - 2 4x² + 4x + 17 dr

A: Breaking the numerator is the key here. After that, break the given function into two parts and then…

Q: Find an integrating factor for each of the following equations and solve these equations. 1) (x² +…

A: A detailed solution is given below.