For both parts, sketch and shade the 2D region, draw a typical disk/washer, and set up the integral that gives the volume (do NOT evaluate the integral). (A3a) Region bounded by the curves y = e*, x = 0, and y = 3; rotated about the y-axis. (A3b) Region bounded by the curves y = x² and y = x + 6; rotated about the x-axis.

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A: We need to check whether the given series converges or diverges.

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A: Topic = Area

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A: Topic of question - Limit and continuity Given graph,

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A: Answer :- Given ,  The graph of a relation  We have to find the domain and range

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A: The left-hand and the right-hand limit of the function fx as x→a exits and are equal.

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A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

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A: Topic = Coordinate geometry

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A: See this solution in below

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Q: Liner algebra

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A: The function is given by fx = 8x3+3cosx To determine: The derivative of the function f'x.

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A: We will integrate y from 1 to 2 to find the required area.

Q: 4. Solve the differential equation: x(y - 1) dx + (x + 1) dy = 0. If y = 2 when x = 1. A. 1.80 B.…

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Q: Solve the following partial function. dx + e3x dy = 0

A: Given query is to find the solution of the differential equation.

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A: Here we have to plot the graph.

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Q: 1. FIND THE FIRST PARTIAL DERIVATIVES j) f(x, y, z) = y x+y+z k) f(x, y, z)=√√sin²x + sin² y + sin²…

A: This question can be solved using the concept of derivative using quotient rule and derivative of…

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Q: 5. a. If g(x) = f(x) cos x, h(x): find g'(). - f(x) tan x where f() = 14 and f' (²7) : b. find ƒ'…

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