The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

Q: The letters r and 0 represent polar coordinates. Write the given equation using rectangular coordin…

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Q: 1. S 2. [x²e²² dx 3. [sec* (x) dx 4. fxinx dx 5 ( x50x² dv x arccos x dx 6. Jese² (3x) dx 7. fx³ež…

A: Since multiple questions are asked, I am answering first question

Q: Find the maximum and minimum values of the function ㅠ g(0) 60 7 sin(0) on the interval 0, = Minimum…

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Q: Given cost and price (demand) functions and C(q) = 115q + 43000 and p(q) = -2.3q + 900, what price…

A: We have, Marginal profit (MF) = Marginal Revenue (MR) - Marginal Cost(MC)

Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

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Q: 1 x√x²+3 (A) Use trigonometric substitution to find f

A: Use  trigonometric substitution to solve the integral.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: We can solve this as follows:

Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given po…

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Q: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

Q: 20. √9-5x² X -dx

A: SOLUTION-

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. X₁ 1 y=6 1…

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Q: What is the derivative of y = √5x² + 3x + 2 where x = 1? O no correct answer O2.054 O 2.057 O2.056 O…

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Q: The derivative of f(x) with respect to x is the function f'(x) and defined as f(x+h)-f(z) f' (z) =…

A: topic- derivative of a function

Q: What is the second derivative of the function y = -7 sin x cos x where x is ? Round your answer to…

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Q: Given the function f(x) = 5x(sin x + cosa) what is f' (4)? O No correct answer O -1.996 O -2.99 Ⓒ…

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Q: Question 12 ( What is the function of cos that has an amplitude of 4 a period of at (0,2)? and has a…

A: Given:  Amplitude = 4   Period = 2π  POINT : ( 0 , 2 )

Q: Consider the following vector fields: F = (3x²e²ª, 2x³e²y + 2 cos y sin y) and Ġ = (y+z, x+y, z —…

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Q: Consider the solutions Y(t) of with a, b, d constants and a, b>0. Calculate lim y(t). t-x Hint:…

A: This question can be solved using the concept of linear differential equation and limits.

Q: At least one of the answers above is NOT correct.. Consider the mixing process shown in the figure.…

A: According to the given question  In flow  Clear liquid  = 10 L/min Dye solution = r  L/min, having…

Q: If a set S has both a minimum and a maximum, then S is closed.

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) I sint sin(t)√1 + cos(t)…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: After…

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Q: Find the absolute maximum and minimum values of the function f(x) = cos²x-3sinx on the interval…

A: Given function, f(x)=cos2(x)-3sin(x) We know that, Suppose that x=c is a critical point of fx then,…

Q: Gi‎ven: ∫ 40∫ 4−z0∫ 2√y f (x, y, z) dx dy dz a. Sk‎etch the so‎lid of integr‎ation of the give‎n…

A: Let's solve.  1.   Sketch the solid.

Q: Determine the absolute extrema of the function f(x) = (x-3)ex on the interval -1≤ x ≤ 3.

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

A: Given that A projectile is launched straight up in the air. Its height t seconds after launch is…

Q: f(x)= (4x² +8x+2)

A: We can find the derivative using chain rule as below.

Q: Find the total area under the curve f(x) = 2xer² from a 2xe from x = 0 and a

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) I COS(π/X⁹) dx X10

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. - eu du (6 - e4)²

A: topic- indefinite integral

Q: he function f(x) - 2x³ 30x²+144x + 6 has one cal minimum and one local maximum. Use a graph of the…

A: Please refer to the image below

Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Suppose that f is a function given by f(x) = 2x + 7. Which is TRUE about the function? ET O None of…

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Q: 2t³ +11t+8 3 t³+4t² +4t 7. S -dt

A:

Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = sec about the…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. tan(2x…

A: The given function  tan(2x+y)=2x

Q: 13. (2x³ +9x) dx ²+3)(x² − 2x+3)

A: Given

Q: Find the characteristic equation, the eigenvalues,

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Q: Determine the constants a and b in the equation of the curve y = ax + b³ + ca+d having a critical…

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Q: Given compute the following integral. [ f(x) dx = -9 and 1.° 8f f(x) dx = -8, в' 8f(x) dx

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: Evaluate the double integral over the rectangular region R. x√9 - x²dA R = Mi [[ x√√9 – x²dA; R =…

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Q: Put the equation that is in general form: y = x² + 22x + 112 into standard form: y = (x − h)² + k:…

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Q: (2xy-sinx) dx + (x² - cosy) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: Consider the function f(x)= = x² + 7x + 12 -2 a. Find the first derivative. f'(x) = b. List any…

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Q: Determine the constants c and d in the equation of the curve y = ax + b³ + ca+d having a critical…

A: The objective of the question is determine the value of c,d on the given curve.

Q: O C. Z= (sin O D. Z= (cos + i cos Write the complex number 9-9√3 i in exponential form. z= (Simplify…

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Q: What is the derivative of y = (-3x²-x+4)e5 ANSE

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Q: 1 x √x²+3 igonometric substitution to find f

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Q: Solve the equation for z = C: i(z - 2i)² = 8 Select one: O a. z E-2, 3 + 4i O b. z € 2,-2 + 4i O C.…

A: