Use a triple integral to find the volume of the solid shown in the figure. z = 16 - x² - y² 10 Need Help? Read It -8-6-4 864 Watch It 2 N 476-8 LY 468

Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Solution is given below:

Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

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Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

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Q: Solve for the solution using variation of parameters: (D2-1)y= 2/(1+ex)

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Q: Describe the graph of the equation. r = 7costi 14 sin tj + k O An ellipse in the plane x = 1, center…

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Q: Describe the graph of the polar equation. 5r cos 0 + r sin 0 = 7 Line with slope 7 and y-intercept…

A: Explanation of the answer is as follows

Q: An ellipse of equation 4x²+2y²=k the distance between its foci 2√3Find the value of k

A: A detailed solution is given below

Q: (1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and…

A: Solution ) Volume of the cylinder    V = πx2h        x = radius         Differentiate with respect…

Q: A 10,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres…

A: As per our guidelines we can answer only 3 subparts of the given equation. Kindly repost the…

Q: 1/2 y = (4x-3)¹/²₂ d³y 3 dx

A: Third derivative id given.

Q: Find the area of the region between the curves y = 12 - x² and y = x² – 6. Area between curves =

A: To find the area between the given curves

Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Value of x for which series is convergent is given.

Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact…

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Q: Consider the series (3x)" n n=1 Find the interval of convergence of this power series by first using…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A: answer is in next step

Q: Suppose that f(x) and g(x) are given by the power series f(x) = 6+7x+7x² + 4x³ +….. and g(x) =…

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Q: IF F. dr. F(x, y) = 9xi + 6yj C: r(t) = ti + √4-t²j, -2 ≤ t ≤ 2 Evaluate

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Q: 3. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that has a…

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Q: Find the value k that makes the function continuous. kx 10, x 10 M > f(x) = _ 4x + 10, x < 10 Submit…

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Q: Part a) Plot the point given in polar coordinates. (-3, 2pi/3) Part b) Find three additional polar…

A: answer is in next step

Q: Solve the D.E ý - 25 +2y = 2X+3

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Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t) ||³ = r(t) = e³ti + e-tj to find k(t).

A: By using the formula kt=r't×r''tr't3 to find kt.rt=e3t i+e-t j

Q: differentiate using delta method y= x2-6x+8

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Q: Find all solutions of the equation in the interval [0, 27). (Enter your answers as a comma-separated…

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Q: I sold something on ebay and I go to the UPS store to ship the package. The cost for the box is $3,…

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Q: Which of the following is the derivative of (x³ + 1)(x² + 2x)? 3x²(x² + 2x) + (x³ + 1)(2x + 2) 3x²…

A: This question is based on product rule of differentiation.

Q: f(x) = ((3x + 7) if x ≤ 4 ax-1 if x > 4

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Q: 1. Find the area between the curve y=x²+2 and the x-axis, between x=1 to x=3

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs x = y³ and x = y…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) [0, 6] x2

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Q: Solve the initial value problem. Y 6 dy dx 2xy = 8x, y(0) = 5

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Q: The graph y=f(x) is given; transform the graph y=f(x) into y=2f(x+1)

A: Given: Line passing through 0, 0, 4, 4:  y=x    {0≤x≤4}The equation of the curve is y=x-52+3…

Q: Find DO NOT SIMPLIFY YOUR ANSWERS. 1. log √2x² + y + 2x² + y) + tan(x™ — ñ³) = sin¯^¹²(x² − 1) + ½ /

A: To dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: 3 find the values of az/ax and az/ay xe³+ ye² + 2 lnx-2-3 In 2 = 0, (1, In 2, In 3)

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Q: If In a 2, ln b = 3, and ln c = 5, evaluate the following: = (a) In (10-2) = b-4c² (b) In √6-³c-²a-1…

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Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?…

A: The error in the approximation of a given series is always less than the last term that is used for…

Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table.…

A: To find out the tangent line approximation.

Q: Determine the interval of convergence for the series 2¹.¹. n=0 The series converges on the interval…

A: This is a geometric series with r=2x.

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. [²4x³…

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Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: Evaluate the function at the given values of the independent variable. Simplify the results. g(x) =…

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Q: Write the Taylor series for f(x) = xº about x = −4 as Σ Cn (x + 4)". n=0 Find the first five…

A: The given function is  f(x)=x3 about x=-4.

Q: Determine two coterminal angles in degree measure (one positive and one negative) for each angle.…

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Q: d d Calculate[ri(t) r2(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

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Q: Find the average value of ƒ(x) = x² √√28 + x² on the interval [0,2]. favg= Report all answers…

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Q: Find the work done by the three-dimensional inverse-square field 1 F(r) = r on a particle that moves…

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Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.