Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x² - x³ and y = 0

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A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

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A: SOLUTION-

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A: We have to solve given Questions.

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A: Given :u→ and v→ are orthogonal

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A: Given problem:- Consider the position function s(t) = - 16t2 + 96t representing the position of an…

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A: We have to draw the direction field for the given differential equation.

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Q: 5.) I. b -3 -6 Simplify. Write "undefined" for expressions that are undefined. S + toom 6 0

A: Answer (5) We have to simplify

Q: Typewritten for an upvote. No upvote for handwritten. Please skip if you have already done this

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A: This question can be solved using the concept of linearization of function.

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Q: (a) Find the general solution of each of the differential equations: dy 8e2x - 4x dy dx = 12e - 10y…

A: Solved below.

Q: Evaluate S ( + - + e²+ =) dz 3 · 3z 21² In x++²x+}x+ + C Option 1 √√(x³)x= √√√x + √2x+C I- Option 2

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Q: Please

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Q: 7. Find the general solution to the differential equation 2²y+2y=2¹/¹/2

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Q: 11. Given f(x, y) = 6r² - 2r³ + 3y² + 6ry. Determine any local maxima, local minima, and saddle…

A: To find out the local maxima, local minima and saddle points.

Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

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Q: Apply Green's Theorem to evaluate the integral. $(3y + x)dx + (y + 5x)dy C: The circle (x - 3)² +…

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A: The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take y…

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A: This question can be solved by the concept of limits and definite integrals.

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A: Answer: True

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Q: 1. I. Evaluate each determinant. -5 -3 3 -4

A: Given,            -5-33-4

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A: Use double integral concept

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Q: I. 7. Evaluate each determinant. -3 4 -5 2 -3 -5 1 5 3

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Q: 8. Use the given graph to estimate the left Riemann sum for the given interval with the stated…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: e. 4 e2z 1+etz dz

A: topic- definite integral

Q: 5.) Simplify. Write "undefined" for expressions that are undefined. -2 -3 THE -6 -3 M

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