Find the area bounded by the curve x² = y and the line y - 4 = 0.

Q: Find the area of the region enclosed by the following curve x-y²= 0 and x + 2y² = 3

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Q: Find the total area of the rectangles in the figure below, where the equation of the line is f(x) =…

A: The equation of the line : f(x) = 2x – 12Find the total area of the rectangles in the figure below :

Q: 5x Part C: What is the directed distance when = Give an exact answer.

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Q: Consider the function U(x)=(x²-1)In(1-x²). . What is the domain of the function U(x) (i.e., where it…

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Q: Evaluate the integral by changing to spherical coordinates. 4 16x2 32 - x² - y² √² √ √ ²6-*² √222-x²…

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Q: Show that the limit does not exist X lim (x,y)-(0,0)√√x² + y²

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Q: 3. Trace the curve: y² = x³ + 4x² - 9x - 36

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Q: Find the maximum and minimum of the following function f(x) = 2 + x^(2/3) determining the intervals…

A: find the derivative and equate it to zero. it cannot be zero.Therefore, the endpoints are x = 0 and…

Q: If the cost, C, for manufacturing x units of a certain product is given by C=x²-20x+45, find the…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 29: Area enclosed by y² = 5x, y2 = 0 and y-axis is?

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Q: The function f(x) = 2x³ - 24x² + 72x + 3 has one local minimum and one local maximum. You may use a…

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Q: Solve the given initial-value problem. y(t): d²y - 4 dy5y= 0, y(1) = 0, y'(1) = 5 dt² dt

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Q: For Osrs 1, the solid bounded by the cone z=3-3r and the solid bounded by the paraboloid z=3-3r²…

A: The solution is shown in step-2

Q: At which angle is seco = √2? 7x 6 5x 4 7″ 11/ 6

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: Find the value of n that satisfies the expression for the function y = 2x5 + 3x4 + 4x³+5x² d'"y dx"…

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Q: Find the indefinite integral. (Use C for the constant of integration.) [x√³ x√5 - x dx

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Q: Solve the given boundary-value problem. y" + y = 0, y'(0) = 0, y'(π/2) = 0 y(x)

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = x6 e-x (a) Find the…

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Q: A faucet is filling a hemispherical basin of diameter 60 cm with water at a rate of 2 Lit/min. Find…

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Q: rue or False: The equation (x−8)2 / 41 + (y+1)2 /25 = 1 is the equation of the ellipse with…

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Q: Let y = − 3/2 x^2 + 9x − 15/2. Find the absolute maximum and absolute minimum of the curvature…

A: Now, to find the absolute maximum and absolute minimum curvature of the function  on the interval ,…

Q: Find all the second partial derivatives. T = e-2r cos(0) T Tr ГӨ T ar T 00

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Q: Use the Chain Rule to find the indicated partial derivatives x = s + 2t - u, y = stu²; when s = 4, t…

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Q: dP = The population of a town is growing at a rate given by 78 - 6t people per year. Find a function…

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Q: Suppose that functions f and g and their derivatives with respect X to x have the values shown to…

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Q: 1. To rationalize the numerator of multiplied by? a) 8√x + 27 3x b) -8√x-27 what value should the…

A: (1) To rationalize the numerator of , to determine the expression by which the numerator and…

Q: For the demand function q = D(p)=√√301- p, find the following. a) The elasticity b) The elasticity…

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Q: Let f(x) = 2x³ + 3x² - 120x-5. a. Find all points on the graph of f(x) at which the tangent line is…

A: Slope of the tangent line at a point to a function is the derivative of the given function at that…

Q: Find the general solution of the given second-order differential equation. 18y" - 9y5y = 0 y(x) =

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Q: 4 a₁ = -1, and a =for n = 2, 3, 4, ... What is the common ratio, r, for this sequence? n-1 O r = -1…

A: …

Q: The weekly marginal cost of producing x pairs of tennis shoes is given by the following function,…

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Q: Find the derivative the function f by using the rules of derivatives. 5x½ 4 a. f(x) = fƒ'(x) = b. f…

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Q: Find the derivative of y with respect to x. 1 -1 √/9x² −1+ sec¯¹3x, x> 2 3 y = cot

A: we have given function To Find: find the derivative

Q: Find all the second partial derivatives. = sin(2s² - 3t²) V ss V st V ts V tt = = =

A: To find all the second partial derivatives.

Q: Consider the helix r(t) = (cos(2t), sin(2t), 1t). Compute, at t = 픔 in (2-7) √5 A. The unit tangent…

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Q: Consider the path r(t) = (4t, 2t², 2 lnt) defined for t > 0. Find the length of the curve between…

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Q: Find the particular antiderivative that satisfies the following conditions: F(x) = F'(x) = x³ +5√√x;…

A: Given:We are required to find:

Q: Find all the relative extrema (local extrema) and the saddle points of the function f(x, y) = (y²…

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Q: 8. Be sure to show and explain all steps. Determine lim X→C 2f(x) - 3h(x) (g(x)) + (h(x))² lim_ f(x)…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Find the derivative of f(x) = −4x6√√x+ 4 x ³√√√x Make sure to show your work neatly and attach to…

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Q: Determine the convergence or divergence of the series. (If you need to use oo or -00, enter INFINITY…

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Q: 2 16 sin *x cos x

A: Given, the expression 8sin2xcos2x. We have to write this expression in terms of trignometric…

Q: Evaluate the surface integral. Jy d y ds, S is the helicoid with vector equation r(u, v) = (u…

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Q: Problem. 7: Find the linear approximation of the function f(x)=√x +3 at a = 22 and use it to…

A: Therefore linearization at a = 22 is,

Q: Use cylindrical coordinates. Evaluate III. x2 dv, where E is the solid that lies within the cylinder…

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Q: Find the general solution to the following system of DEs using eigenvector methods. 6 -7 -(i-1) x -2…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: y(t): d²y4dy - 5y = 0, y(1) = 0, y'(1) = 5 dt² dt

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Q: If the daily cost per unit of producing a product by the Ace Company is 25+ 0.2x dollars, and if the…

A: given data daily cost per unit is 25+0.2x dollars given price is $80