The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = x. Find the area of th writing a as a function of y and integrating with respect to y. УА 1 0 y = 1 y = √√/x X

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A: Evaluate the integral ∫171x3+1dx a) Midpoint rule b) Trapezoid rule  c) Simpson's rule

Q: Please solve and show all work. Let y = (x² + 1)³. Find the differential dy when x = 2 and dx = 0.4…

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Q: 1. Write the vector in components form. 1) RS where R=( 3,7) S = (8,-1) A) C) B) D)

A: Given, R(3,7) & S(8,-1)

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A: Equation of a straight line with x-intercept a and y-intercept b is defined as xa+yb=1 Therefore,…

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A: The given trigonometric equation sin θ=-67. We have to find the solutions in the interval [0, 2π).

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Q: the exact answer. 1 The area of a quarter circle is -πr²

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Q: Find the area between the curves: y = x³ - 11x² + 28x and y = -x³ + 11x² - 28x

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Q: Find the maximum for the profit function, P = 15x + 25y subject to the following constraints. 3x +…

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Q: The region R in the first quadrant is bounded by y = 8 sin(2), y = 8(x - 2)² and y = 5x + 3, and…

A: As per Bartleby guideline We will solve the first three questions. Area of region bounded curves: if…

Q: The average cost function for a particular business that sells toys is represented by 4(x) =…

A: To find the average cost for large amount of toys.

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Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

A: For solving the given problem:

Q: 5x² 이 sin (8x) dx = 5 1 xcos(x) + 1 256 (8xsin(x) + cos(8x)) + C

A: We need to integrate: ∫5x2 sin8x dx We can solve this using integral by parts.

Q: Find all the zeros of the function h(x) = 4x³ + 23x² + 34x-10 +i,- O3+1,-3-i O-1-3+1-3-1…

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Q: Find the surface area of the part of the plane z = 7+ 3x + 4y that lies inside the cylinder 2

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Q: Question 5 Solve x4y (4) + 6x³y (3) + 25x2y + 19xy' + 81y=0 where x > 0 c cos (31nx) + c sin (31nx)…

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Q: Describe the region whose area is given by the integral r3 S Same 3 sin 0 r dr do.

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Q: 3 Solve the above system by any algebraic method to find the values of x and y then select the…

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Q: Lea wants to build a compost bin in the backyard but is only using the area beyond the path running…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

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Q: Given f(x, y) = sin(x + y) where x = s³t², y = 38 - 2t. Find f.(x(s, t), y(s, t)) = f(x(s, t), y(s,…

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Q: Find the directional derivative of the function f(x, y) = ln(x + y³) at the point (-3, 1) in the…

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Q: Evaluate the first partial derivatives of the function at the given point. f(x, y) = 9e* In(y); (0,…

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Q: .Evaluate the integral of (3x +9y) dx dy if the interior limits has an upper limit of y and a lower…

A: Let's consider the integral as given below: I=∫ab∫cdf(x,y)dxdy---1 Where f(x,y) is function of two…

Q: dy dx general solution y as an explicit function of x. (ii) What is the particular solution…

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Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A: t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v(ft/s) 0 6.7 11.2 15.5 18.8 19.8 20

Q: Compute the coefficients for the Taylor series for the following function about the given point a…

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Q: Given f(x, y) = 3x - 5x²y³ + 4y², find fz(x, y) = 123-10xy³ fy(x, y) = fax(x, y) = fry (x, y) =…

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Q: . The critical point of f(x, y) = 4x² +9y² + 8x − 36y: A. Occurs at (-1,2) and is a local minimum B.…

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Q: derivative its actually only cos^12 on the last idk why

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Q: A line passes through the points (5,2) and (3,7) A. Find slope. B. Find y intercept. C. Find the…

A: Given that two point (5,2) and (3,7) and we find slope and y intercept and equation of line.

Q: Q.1. A radioactive substance decays in such a way that the amount of mass remaining after t 0.011t…

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Q: What is the final value of the following postfix expression: (Hint: You can draw a tree if it helps…

A: 9 3 / 5 + 7 2 - *

Q: Use the Divergence Theorem to evaluate the flux of the field F(x, y, z) = (x + z², xz + y², zx - y)…

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Q: For the given function and values, find Af and df. (Round your answers to three decimal places.)…

A: Given function f( x , y ) = x2 + xy + y3x = 2 , ∆x = dx = 0.7y = 1 , ∆y = dy = -0.1

Q: What is the area bounded by the curve y = x³, the x-axis and the line x = -2 and x = 1? A. 4.25 B.…

A: To find the area bounded by the curve y=x3, the x-axis  and the line x=-2 and x=1.  Note: Since the…

Q: The diameter of each wheel of a bicycle is 26 inches.

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Q: For the function of three variables, find the partials fx, fy, and f₂. 1 = (x² + y² +2²)* f <<= =…

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Q: s' (x²+i) 3 xdx

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Q: If d²₂ y dx2 y(1) = 2x , then a general solution is y(x) = x³+Cx+D. Find the value of the constant D…

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Q: Let W be the region between the sphere of radius 5 and the cube of side 1, both centered at the…

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Q: Use Green's Theorem to evaluate [ F F.nds, where F = (√x + 6y, 5x + 6y) C is the boundary of the…

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Q: Practice 1. Solve the following polynomial inequalities, XEIR. a) b) c) d) e) f) g) h) i) x²-4x+30…

A: a)x2-4x+3&lt;0

Q: The integral of cos x with respect to x is A. sin x + C B. sec x + C C.-sin x + C D. cScx+G X+C

A: We find integration of cosx and cos(2x)e(sin2x).

Q: A company determines that its marginal revenue per day is given by R'(t)- 100e¹, R(0) -0, where R(t)…

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

A: The function is fx=6xx2+2, 1≤x≤3.