Write the equation in spherical coordinates. (a) 7z² = 8x² + 8y² (b) X x² + 4z² = 4

Q: 5. A sphere has equation x² + y² + z² = x. What is the equation of the sphere in spherical…

A: equation of the sphere x2+y2+z2=x

Q: 11. Given the graph of f(x) below, describe the type and location of all discontinu 4 f(x)

A: Limit and discontinuity

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Q: b. Find the MacLaurin polynomial of degree n for f(x) = x+1

A: Maclaurin and Taylor theorem.

Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

A: R'x=0.03x2-0.05x+216  Find the demand function px

Q: Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to…

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Q: 4. Set up an integral in spherical coordinates for the volume of E, where E is the solid top-half…

A: Given that, E is the solid top-half hemisphere defined by              0≤x2+y2+z2≤9    and  z≥0.…

Q: Will has a bag of gumdrops. If he eats 2 of his gumdrops, he will have between 2 and 6 of them left.…

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Q: 4.2 Find the area of the region bounded by the curves ª 9x² and xx 9x between -3 ≤ x ≤ 3. Show all…

A: We have given two curves and we have to find the area of the region between curves.

Q: Let F(t) = Find a parametric equation of the line tangent to r(t) at the point (157, 16, 4.159)…

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Q: use the Alternating Series Test to determine if the series converges. If the Alternating Series Test…

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Q: Integrate f(x,y,z) = x + √y - 2² over the path from (0,0,0) to (1,1,1) given by C₁: r(t) = ti+t²j,…

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Q: All units in a 100-unit apartment building are rented out when the monthly rent is set at r =…

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Q: Solve the given initial value problem. y" - 4y" +10y' - 12y=0 y(0) = 1, y'(0)=0, y''(0)=0 y(x) =

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Q: Locate any extrema of the function f(x) = 2x2". State only the EXACT x-value of th extrema.

A: f(x)=2x2x

Q: Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal…

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Q: Evaluate the integral. 1 4л Зл SS S y sin z dxdy dz 000 1 4л Зл | | | ysinzdxdydz | y sin z dx dy…

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Q: Evaluate the indefinite integral. Use C as your arbitrary constant. 5x6 +17x8 - 20x9 78 1³ dr

A: we have given the integration ∫5x6+17x8-20x9x8dx

Q: Q6. Using u = dy, the second order ODE: ²-yd = 2(x) dx dx is reduced to the following first order…

A: The second order ODE  (d²y/dx²)-y(dy/dx)=2(dy/dx)³

Q: sketch the function y=(x+3)^(3)-1, and its inverse. Is the inverse a function

A: We have given a function and we have to sketch and find its inverse.

Q: 11. For the following initial value problem, compute the first four approximations U₁, U₂, U3, U4…

A: The solution is shown in step-2

Q: ind all the first and second order partial derivatives of f(x, y) = −10 sin(2x + y) — cos(x - y). af…

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Q: find the integral from bounds 3 to 8 x/3x^2-9 dx WITHOUT using u substitution or anything similar

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Q: Use the transformation u=3x+4y​, v=x+4y to evaluate the given integral for the region R bounded by…

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Q: Find f such that f'(x) = 8x-9, f(7) = 0. f(x) = 0

A: f'(x)=8x-9, f(7)=0

Q: Find the curvature of the curve r(t) = (4 cos(3t), 4 sin (3t), 2t) at the point t = 0 Give your…

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Q: Use the table of values to evaluate the expressions below. x f(x) g(x) 0 4 7 1 2 3 2 8 6 3 6 0 7 1 0…

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Q: ASIC Compute R6, L6, and M3 to estimate the distance traveled over [0, 3] if the velocity at…

A: Reimenn sum of integral

Q: Use the appropriate methods to solve the following integrals. a. So 0.5x e te e2x dx

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Q: S (x+3)√(x+3)² – dx = sec¹()+c

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = t-√√t, [-1,…

A: ft=t-t3

Q: Find the centroid of the plane region bounded by the x-axis, and by the curve y = √4-r².

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Q: Find formulas for (f + g) and (f - g). f(x)=x²-10x+25 and g(x)=x²-10x + 24 (f + g)(x) = [?]x² +…

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Q: Calculate a b, where a = 5i + 10j + 5k and b = -8 -8i + j + 17k. (Use symbolic notation and…

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Q: Find the 3rd derivative of y = e³x - x³ when x = 0.

A: y=e3x-x3

Q: -1 1.0 -1 110 8

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Q: Suppose z = x² sin y, x = -4s² + t², y = -2st. A. Use the chain rule to find and as functions of x,…

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Q: Logarithmic and Exponential Function. Find the derivative of f(x) = ln(sin

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Q: The average worker at Wakefield Avionics will have assembled N(t) = −4t3 + 24t2 + 4t (0 ≤ t ≤…

A: Given that , Nt=-4t3+24t2+4t , 0≤t≤4 How many hours into this shift is the average worker performing…

Q: If f is the function whose graph is given by 2 which of the following properties does f have? A.…

A: A graph of the function is given. We have to identify the correct statement about the function.

Q: Convert the point (p, 0, 6) = 4, Calculator 5п п 3' 3 expressions, or decimals to at least one…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the first four nonzero terms in a power series expansion about x=0 for the solution to the…

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Q: Find the general solution to this third-order ODE of undetermined coefficients: y" + 3y" + 3y + y =…

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Q: Solve the nonlinear inequality. Express the solution using interval notation. x²-x-12 (3x - 2)² ≤0

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Q: Suppose f(x, y): = 2 and u is the unit vector in the direction of (2, -1). Then, x² + y² (a) ▼ f(x,…

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Q: Evaluate the integral. 1 SI letti i + (t+e²¹)j + (t²- sec²t) k di | di t² +1

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Q: The concentration, C, of phenylbutazone, in micrograms per milliliter (µg/mL), in the plasma of a…

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Q: apply the Limit Comparison Test to determine whether the given series converges or diverges. 2n 3n+1…

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Q: Convert the point (x, y, z) = (-1, 2, 0) to cylindrical coordinates. Give answers either as…

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Q: Determine whether the infinite series 3n² n+4. Σ tan n=1 converges or diverges, and if it converges,…

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