f(x)=4-x², y = 4, x = 2 Find the volume of the solid obtained by rotating the region A about the x-axis.

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

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A: Graph the parabola y=(x^2-100x)/50

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A: Differential equations

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A: This question can be solved using the concept of integration by substitution.

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A: Given problem:-

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A: Explanation of the answer is as follows

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Q: Find t for the following terminal points, 0 ≤ t < 2π (a) P(0, 1), = √2 2 (b) P ( - 1/², 1/²³). 1 = t…

A: Let's find t for the given  terminal points.

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A: Given,       u=cosφ     du=-sinφdφ -du=sinφdφ

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A: Here we have to choose the correct option.

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A: In this question, we want to know the domain and range of the given function.

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 7 sin(x) + 7 cos(x),…

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Q: A) Find all value(s) of a such that lim f(x) does not exist [Select] B) Find all value(s) of b such…

A: Question 8 A) limx→1-f(x)=6≠limx→1+f(x)=4 limx→2-f(x)=-∞≠limx→2+f(x)=∞ answer: a=1 and a=2 only

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A: The given function f(x)=-2x3+6x2+172x-3

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Q: (c) Find the Inverse Laplace transform of the function. 1 s² + s-5 H (s) = (s−2)² +3 s (s² + 2s + 5)…

A: Given H(s)=1(s-2)2+3+s2+s-5s(s2+2s+5)To find Inverse Laplace Transform.

Q: B3. Find the integrating factor by inspection then solve.  ydx + (x + x4y2)dy = 0

A: Let's solve given diffrential equation.

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A: Note: as per guidelines we support one question in one request . kindly repost next question in next…

Q: given the following equation: 36y^2-4x^2=144.  a) determine if the function is an ellipses or a…

A: This question can be solved using the concept of conic section.

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Q: 4) Find equations for the planes: b. The plane through (1.–1,3) parallel to the plane 3x+y+z=7

A: Given problem:- Find equations for the planes:   b. The plane through (1.-1,3) parallel to the plane…

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Q: an integral corresponding to the area of the region bounded by the curves of the functions f and g…

A: f(x) =x2 -4x  g(x) = -x2 here area function = f(x) - g(x) = x2 -4x  -(-x2 ) = 2x2 - 4x

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A: To solve: The equation log3x-9+k=2-log3x-1+k. Given: The value of k=3 Concept used;…

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Q: Solve the given initial value problem. x³y² - y³ = 45 ³y² + xy³ = 18 x²y² + xy³ = 90 x¹ y² + y² =…

A: Here we have to solve the differential equation.

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: topic- average value of function over interval

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A: Given problem:-