Use spherical coordinates. Find the volume of the part of the ball p ≤ a that lies between the cones p = and p = w/ = 3

Q: d(x,y) a. Solve the system u = 3x + 2y, v=x+4y for x and y in terms of u and v. Then find the value…

A: u=3x+2y,v=x+4y

Q: 2: Find the Maclaurin series for 2². 2²² = ∞ n=0 ?

A: f(x)=2x2

Q: In a normal deck of cards, with 52 cards creating four suits including hearts, spades, diamonds, and…

A: In a normal deck of cards with 52 cards creating four suits including hearts,spades,diamonds and…

Q: 3 -6 21 Find a basis for column space of A = -2 1 -2 - 14 7

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Q: Calculate the double integral. JJ 7x sin(x + y) dA, R= [0, 1] x [0] 0, 3

A: ∬R7xsinx+ydA,R=0,π6×0,π3

Q: f(x) and its linear approximation (i.e., its tangent line) change value when a changes from to xo +…

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Q: Let f(x) = x³ + 9, g(x) = x² − 7, and h(x) = 2x + 6. Find the rule for the function. fg h

A: I am attaching an image so that you understand each and every step.

Q: Find the indefinite integral 1 12 X 12 X 1 5 1 1 12 [(-²). 12 5 dx = dx.

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Q: Let y = tan(4x + 5). Find the differential dy when x = 2 and da 0.4 Find the differential dy when x…

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Q: Verify the formula by differentiation. √5x+8² −dx = In |5x+8| + C, x‡ The G|00 5 can be used to…

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Q: Find the antiderivative for each function when C equals 0. Check your answers by differentiation.…

A: Given;

Q: Use spherical coordinates. Evaluate JJJ √x² + y² + z² dV, where E lies above the cone z = x2 + y2…

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Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

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Q: Find the equation of the tangent line to y=xat x=4 X+2 y= 4

A: Application of derivative

Q: Find fxxx for f(x, y) = Sin() at (π, π)

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Q: Calculate the 3 x 3 determinant. (Use symbolic notation and fractions where needed.) -6 6 9 -5 8 9 =…

A: let  K=-669-5894-38

Q: 1 as Compute the first four partial sums S₁, ..., S4 for the series having n th term an starting…

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Q: Find the surface area of the part of the plane z = [1, 5] × [0,5] = 2 + 4x + 3y that lies above the…

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Q: 9. Evaluate each limit, if it exists, using any appropriate technique. 16 - x² 14x3+64 a. lim x²16…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 9…

A: The given double integral is  ∫09∫081-y2(x2+y2)dxdy We have to change the Cartesian integral into an…

Q: 37) Answer with full steps: A rover on Mars has just collected a very interesting soil sample. It…

A: The distance above the surface of the mars that the rocket carrying the sample after t hours is…

Q: S dx= In |5x + 8 + C, x# 5 5x+8 -85 The definition of an antiderivative can be used to verify the…

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Q: Evaluate the indefinite integral below. (z² - 4)² dz

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Q: =√(y-3), 1<y≤9. x =

A: We know that the exact length formula int_a^b sqrt(1+(dx/dy)^2) dy

Q: The following graph is the graph of a function.

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Q: Consider z² + xyz + y² = x² + 6z + 24, where = f(x,y). a) Using the Implicit Function Theorem (not…

A: Using partial differentiation

Q: Solve the triangle given ZA = 36°, ZC = 69°, b = 18: ZB= a = C = O Round the answer to the nearest…

A: given ∠A=36°∠C=69°b=18

Q: g(x) = marctan(x) x) = h(t) = arcsin (8t + p). (t) =

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Q: An object is moving with velocity (in ft/sec) v(t) = t² — lt + 1. At t = 0, the object has a…

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Q: a) What is the z-component of a vector parallel to the xy-plane? Explain. b) Find all unit vectors…

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Q: Please make the answer easy to read

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Q: GRAPH and find the length of the curve   A. (x^5)/6 + 1/(10x^3) 1<=x<=2   B. y^2=4x 0<=y<=2

A: Since you have posted multiple questions, as per guidelines, we are supposed to answer only first…

Q: You were given the function f(x) = 5x² + 10 and asked to determine the intervals on which the…

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Q: Let P(t) give the total number of people getting a particular disease t days since the disease was…

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Q: 0 is an angle in standard position whose terminal arm is in 3 Find sin 8. /13 quadrant IV and cos 0…

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Q: f f(x) = ex − 1, 0 ≤ x ≤ 2, find the Riemann sum with n = 4 correct to six decimal places,…

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Q: 4 Find the general antiderivative of f(z) = √2³. Use C for the constant of integration. F(z)= =

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Q: 75

A: Marginal profit refers to the profit earned from sales of an additional unit. To find profit,…

Q: Find formulas for f/g and g/f. f(x)=√x-2 and g(x)=√x +4 || 460 60/4 11 f √x²+[?]x-8 X + x² + 2x - X-

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Q: Consider the function f(x, y) = zy- 4y - 16x+64 on the region on or above y = z² and on or below y =…

A: First, we find the critical points of f(x,y) in the given region. To do this, we take partial…

Q: Consider the points (1,3) and (4,4). Find the equation of the line through the origin that the Sum…

A: The perpendicular distance between a point (a, b) and a line y = mx + c is given by, d = |ma - b +…

Q: a) State the definition of fx (xo, Yo) using limits for a function z = f(x,y). b) Given z = f(x, y)…

A: (a) To state the definition of fxx0, y0 by using limits for a function z=fx, y. (b) Given z=fx,…

Q: Use the Law of Sines to find the indicated angle 8. (Assume ZC = 65°. Round your answer to one…

A: Given: We are required to find: θ

Q: Find the volume of the given solid. bounded by the cylinder x² + y² = 16 and the planes y = 2z, x =…

A: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=2z, x=0, z=0 in…

Q: Rolle's Theorem on the

A: Given that fx=cos2x   The three conditions for Rolle's Theorem to hold on the interval a,b are: 1.…

Q: Find the general antiderivative of f(x) = ³. Use C for the constant of integration. F(x) =

A: f(x)=π3

Q: Let y = (x² + 1)4. Find the differential Find the differential dy when = 2 and da x = 0.3 dy when =…

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Q: Draw the spin field F = - 3y √x² + y² -i+ 3x j along with its horizontal and vertical components at…

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Q: Find dy/dx and d²y/dx². x = et, y = te-t dy d²y dx² 11 11 For which values of t is the curve concave…

A: x=et, y=te-t

Q: Evaluate sin x -dx. 2 -1+ cos²x

A: Integration.