Q2 A rectangle is inscribed under the curve a² + 4y2 = 1 with its base on the x-axis, as shown in the figure below. Find the coordinates of (x, y) that will maximize the area of the rectangle. Show all your work. y 1/2 -1/2 (x,y) 1 x

Q: A find the dy dx y = (x²1nx)4

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Q: LARCALCET7 13.9.005. Find the minimum distance from the point to the surface z-√9-2x-2y. (Hint: To…

A: Given ,  Equation of surface z = √(9-2x-2y) We have to find minimum distance from the given point…

Q: 3. Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x -6y + 2z = 5.

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: f(x) = √√/x = -²x³12 about the x-axis for 1 ≤ x ≤ 3. .3/2

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Q: is closest to the point (9, 0).

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Q: Find the shortest distance from the point (1, 1, 4) to the cone z = You may round to the nearest…

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Q: Draw the bifurcation diagram for à = (x + 1)(x² – 2.x +r).

A: We are given : Now, the bifurcation diagram for this is :

Q: Evaluate f (3x²y — y²)dx + (x³ - 2xy)dy, where C' is the parabola y = x²/4 from the origin to (2,1).

A: The given problem is to evaluate the given line integral of vector field over the given path C is…

Q: Please carefully find the domain of the function f(x, y, z) = as a familiar surface. 4x²+92²-25y and…

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Q: What is the maximum vertical distance between the line y = x + 20 and the parabola y = x² over the…

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Q: Y = 3.065 x + (-35.96)=0.6451x + 46.92 an/Fear medial ing au of a t from asur oxim bial hat se toc…

A: Y= 3.065x + (-35.96) = 0.6451x + 46.92 We have to find value of f(x)

Q: Sketch the level surface of the function w +z = 9 – r² when w = 0 for z > 0.

A: Level surface of a function  w=f(x,y,z) for w = c are given by f(x,y,z)=c

Q: Solve the equation (tan x + 1)(sin x - 1) = 0 on the interval [0, 2π).

A: (tan x + 1)(sin x - 1) = 0

Q: 5. Find the area of the surface formed by revolving the graph of y = √√x + 2 from x = 1 to x = 8…

A: Area surface generated by rotating a curve y= f(x)  in interval [a,b]  about x- axis  A=∫ab2πyds…

Q: Evaluate I C: x-axis from (0, 0) to (0, -5) and (0, -5) to (2,-5) (2x - y) dx + (x + 5y) dy.

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Q: Use the Midpoint Rule with m = n = 2 to estimate the value for R= [0, 4] × [0, 6]. √ √ ( 3x + 2y) dA…

A: Sol:- To use the midpoint rule with m=n=2, we need to divide the rectangle R into 4 smaller…

Q: 3. Use calculus (derivative and C.N.) to find the area of the largest rectangle that can be…

A: This question is related to conic section .solve in step 2.

Q: Q3 Determine the area of a surface when the curve y==x² 3 1 x², 1<x<3, is revolved about 2 the…

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Q: ƒ(x) = √√x - 12/1x²³/2 about the x-axis for 1 ≤ x ≤ 3. 3

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Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: thể midpoint of the segment with endpoints (3, 6) and (5, -2).

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Q: Find the area of the region included between the parabolas y? = 4(p + 1)(x +p+ 1), and y? = 4(p² +…

A: Here we have to find the area of the region bounded by the two parabolas.

Q: The curve y = r5 + 17x4 + 9x2 – 57x + e – 6 intersects the x-axis at two points as shown in Figure…

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Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Find the cоттоn points of the circles (x + 1)² + (y – 1)² = 5 and x² + y? = 1.

A: Common points of the circles simply means the point of intersection of the given circles.

Q: Thanks for the help. However, the homework program does not accept that as the correct answer. I…

A: By use the shell method to find the volume of the solid generated by revolvingthe region bounded by…

Q: I3D Find y in terms of x. dy passing through (2,5). dx Vx² - 8x + 16

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