Fill in the blanks: 2² + 1 The equation describes an ellipse. The volume of the solid obtained by rotating the ellipse around the x-axis is *Express your answer in decimal form, round off to the nearest ten thousandths with the proper unit of measure. *use = 3.1416 4. 4

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A: To find the Normal vector to A & B.

Q: For which of the series below the Integral Test can be used to determine whether the series is…

A: Recall the integral test:If fx is continuous, positive, decreasing on the interval k,∞ andfn=an…

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Q: 2 Q41 x ² dy- (xy + y ² ) dx = o Q4\x

A: The objective of the question is evaluate the differential equation.

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A:

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A: The region bounded by f(y)=y3, y=1, y=8 and x=0, trhe region revolved about y-axis.

Q: Convert the following double integral to polar coordinates (do not evaluate). 2 √√4-1² X dxdy = 1+…

A:

Q: Find , given y = 5² 6n² a dy dx

A: ddx(5x6ln2(x))We know that…

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Q: Given the function: f(x) = { // x³-1 x-1 if x #1 k if x = 1 What should be the value of k so that f…

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Q: Find the sum of the arithmetic series where n = 60, a = 9, and t60 = 422

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Q: Determine which of the graphs below have Euler circuits. Vo Vg VI 3 m (US S 5 e6 4 33 V3 Ug (US 27…

A: Euler circuit: An Euler circuit starts & end at same Vertex Here in the given problem we have to…

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A:

Q: Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given…

A: Use derivative concept

Q: The Interior angle of a regular octagon has a measure of: CA. 120%. OB. 135% C. 45 D. 60° COC

A:

Q: 3 Find the area between the curve of X = and the y-axis on the interval [2, 5]. 2.749 3.296 4.159…

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Q: dy 4. Solve the initial value problem : (1+x²). -= yx, y(1) = 2 dx

A:

Q: What is the bounded region between the parabola x = -y2 and the line y = x + 6. Round the answer…

A: This question can be solved using the concept of area bounded by two curves.

Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

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Q: Use Newton's Law of Cooling, T = C+ (To - C)ekt, to solve the problem (bonus) 11) A lasagna removed…

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Q: a dy Find given y = 4 In da

A: The given function,   y=4x lnx

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A: We have to find center of mass.

Q: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

A: " According to the guidelines issued by the company we are supposed to answer only one question.…

Q: Which expression below is equivalent to x4 − 4x³y + 6x²y² − 4xy³ + y4 O (x + y)4 (x - y)4 (x-2y)4

A:

Q: How many paths spell MANAGE? A N A A E a) 15 b) 100 c) 10 d) 20 M ΣΖ A E N G A

A: Use: Pascal's method

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A: Explained below

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A:

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Q: ■ Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3)…

A: Distance of a point from plane

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Q: Find the mass and the center of mass of the lamina with density p(x, y) = and occupies the √y x²…

A: Given :ρ(x,y)=yx21≤x≤3 and 0≤y≤4 then

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Q: 31 Matrix A =[42],find Eigen values of A².

A:

Q: A manufacturer of shirts determines that her fixed costs will be 500 dollars plus 9 dollars for each…

A: Calculation of above requirement are as follows.

Q: Evaluate the definite integral. 2 X dx 1 + 4x 0

A: Take (1+4x)1/2 = t

Q: For the curve f(x) = 2-5x +4x², the slope of the tangent is -5 + 8a at the general point where x =…

A: This question is related to tangent to the curve, we will solve it using given information.

Q: B)Evaluate the integrals: i) f/2rdrde, "1/2 ii) f/²/2finx 2² siny dz dy dx.

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Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

A:

Q: Which graph represents the function f(x) =

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Q: Find both first partial derivatives. z = 8y2 sqaureroot x

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1,…

A: We have to solve given Questions.

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Q: 37) 1 Solve the following simultaneous linear D.E. [D+1 12 [+1 10+2 5D=210) = (2-1)

A: