Use the chain rule to find dw dt = dw dt w = In (√x² + y² + z²), x = 8 sin(t), y = 7 cos(t), z = 2 tan(t)

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A: By using the Shell Method to find the volume of the solid obtained by rotating the region above the…

Q: Find the probability. A basket contains four apples and five peaches. You randomly select one piece…

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Q: Determine of the following series { (-1)" n=1 the convergance и 2n+1 or divergence of each

A: We need to determine whether series converges or diverges.

Q: Evaluate. Use reduced fractions instead of decimals in your answer. 7 sec 6x dx = ² S + C

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Q: 1 1 9. C₁=1+₂+3 ²+ Cn + + 1 n

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Q: The series Σ n=1 convergent. (-1) " n 0.9 Select one: O True O False Give your reasons is absolutely

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Q: ππ|2 ff sin(2x)cos(3y)dx dy 00

A: Use the double integral separate the variable

Q: 10) The graph of h(x) is shown below. Find the average value of h(x) over the interval [0, 10].…

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Q: f(x, y) = 9 — x² y4

A: To use the second derivative test, we need to find the critical points of the function first. To do…

Q: Find the first partial derivatives of the function. 4 f(x, y) = x² + 7xy5 X fx(x, y) = fy(x, y) =

A: Given f(x, y) = x4 + 7xy5

Q: Find area of the region under the curve y = 4x³ - 2 and above the z-axis, for 3 < x < 8. area =

A: We know that the area of the function f(x) at x=a to b is  int_a^b f(x) dx

Q: ntervals on and concave down and identify the x-value corresponding to any points of inflection. "

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Q: PRACTICE ANOTHER Solve the system of linear equations. (Enter your answers as a comma-separated…

A: x1-x2=0...............A 7x1-6x2=-1..........................B

Q: Find the angle between the vectors to the nearest hundredth of a degree. p= and q =

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Q: Find the differential of the function. = x ln(y² + 6) dz= Z = ]dx + ( [ Jdy

A: Given: z=xln(y4+6) We are required to find: The differential of the given function.

Q: Write the following expression as a single definite integral of the form f(x) dx. [²_1(x) dx + [³1x)…

A: Given expression is ∫-22fxdx+∫25fxdx-∫-2-1fxdx

Q: L (4 + √36-x²) dx

A: Evaluate the definite integral  We know that the formula int_a^b f(x) dx=int_b^a f(x) dx

Q: A circular swimming pool has a diameter of 18 m, the sides are 3 m high, and the depth of the water…

A: Given: Diameter= 18 m Sides = 3 m  Dept = 3 m  Acceleration = 9.8 Density = 1000

Q: are there any holes for this function,verticial or horizontal asymptotes?

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Q: A vertical pole 32 feet tall stands on a hillside that makes an angle of 17° with the horizontal.…

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Q: British Deficit The projected public spending by the British government for the years 2010-2011 (t =…

A: The projected public spending by teh British Governmnet for the years 2010-2011 (t=0) through…

Q: Suppose [*, f(x)dx = 2, ſª f(x)dx = 7, [*f(a)da = 9. [²² [² (2ƒ(x) — 7)dx= f(x) dx

A: ∫-18fxdx=2 , ∫-12fxdx=7,∫58fxdx=9

Q: Find the interval of convergence of the series O none of them O [-7,7] O (-7,7] O [-7,7) O (-7,7) Ž…

A: We have to find the interval of convergence of the series…

Q: 3. (a) Evaluate each definite integral using partial fractions (b) S x² + x + 1 (x + 1)²(x + 2) dx S…

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Q: 63. bn = 3-4" 2+7.4" n

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Q: Find the derivative of f(x) = -3²x with no answer negative exponents in

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Q: /n³ + 1 n=1 3n³ + 4n² + 2 00 EXAMPLE2 Σ Since an is an algebraic function of n, we compare the given…

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Q: Find a quadratic equation with the given roots. Write your answers in the form Ax2 + Bx + C = 0.…

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Q: Using Double integrals in Polar Coordinates

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Q: 3) Find the area bounded by the parabola x = 9-(y-2)² and the y-axis.

A: We know that area formula int_a^b f(x) dx

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: 7. Determine consistent system, if possible. if each system of planes is or inconsistent. Then solve…

A: Note:- Since you asked multiple questions , according to our policy we can solve only first question…

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Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

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Q: Find the total mass of a 1 meter rod whose linear density 17 function is p(x) kg/m for 0 ≤ x ≤ 1 (x…

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Q: Find the trigonometric form of the complex number shown below. 10i

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Q: Let g(s) es (s³ + 4). 3 a) Find the equation of the tangent line to g at (0,4). y = | b) Find the…

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Q: 9. Find all the vertical and horizontal asymptotes for the following function and indi- cate the…

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Q: If a cup of coffee has temperature 90°C in a room where the ambient air temperature is 22°C, then,…

A: Given that, T(t) = 22+ 68e-t53 We know average value in [a, b] is, Tavg = 1b-a∫abT(t) dt Here, we…

Q: In Exercises 39-42, find dy/dx. - Sv V2+cos³ t dt 39. y = 40. y = -7x² [T²³v 2 V2+cos³ t dt

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Q: Set up an integral representing the area A of the region enclosed by the given curves. y = 5x, y =…

A: The area between the curves y=f(x) and y=g(x) from x=a to x=b is given by the integral…

Q: find a unit normal vector to the surface at the indicated point

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Q: 43. an = 2¹/n

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Q: Given that tan A = 2 and tan B = 1, and that angles A and B are both in Quadrant I, find the exact…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: . Find the distance traveled by the object for the interval 0 ≤t≤ 5.

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Q: Find the anti-derivative of the func f(x) = = sin (₁+x) - Solve initial Value Problem f(x) = *+^, Y…

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Q: 0. Practice similar fxx (x, y) fxy (x, y) = Calculate all four second-order partial derivatives of…

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Q: (c) Now estimate the area under the graph of f using eight approximating rectangles and taking the…

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Q: Find the value of the constant b that makes the following function continuous on (-∞, ∞ if x 8 PL {…

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