Use a double integral to find the area of the region bounded by the cardioid r= 3(1-sin 0).

Q: Maximizing Profits An apartment complex has 100 two-bedroom units. The monthly profit (in dollars)…

A: P(x)=-10x2+1780x-44000for critical point put  P'(x)=0if p''(x)<0,at crtical point than p(x) has…

Q: Find the gradient of ƒ at the indicated point. f(x, y) = 4sin x² + cos 4y; 3 NOTE: Give your answer…

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x)=sin(x) = cos(2x), 0≤x≤n

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Q: Find the critical numbers of the function. f(x) = x³ + 3x² − 9x (smaller value) (larger value) X X…

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Q: & L 3 5 6 List the interval(s) on which the function is increasing: List the interval(s) on which…

A: Concept:When we going left to the right of graph of function if graph of function is going up for…

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 19 tan-¹ P(-20, 20); a =…

A: Consider the function, fx,y=19tan-1yx and point is P(-20,20)

Q: Use the Second Derivative Test to find and classify the critical points of the function f(x, y) =…

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Q: Find the second derivative of the given function. f(n) = e8n-n4-1 f "(n) =

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Q: Suppose dy/dx=3/1+9x^2 and y(pi/4)=2  what is y(3pi/4)?

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Q: Describe the form of the limit. (You might need to rewrite the function in another form.) lim 2 400…

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Q: Your calculator can be used to directly estimate definite integrals. (See the calculator tutorial.)…

A: To evaluate the following integral. ∫234x dx

Q: In the first answer field, write out the derivative using the quotient rule without simplifying at…

A: Given,            fx=sinx1-sinxTo find : f'xWe know that:           The derivative using the…

Q: Find a unit vector in the direction in which f(x, y) = 33 – 3x² − 3y² decreases most rapidly at…

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Q: Use L'Hopital's rule to evaluate the following limit. The format below allows you to enter the…

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Q: Evaluate the integral. 8e8t S S 2+ e8t 8e8t 8t 2+e dt = dt

A: ∫8e8t2+e8tdt

Q: A spherical snowball is melting. If its volume is decreasing by 450m cubic centimeters per hour when…

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Q: Use a linear approximation (or differentials) to estimate the given number. -0.015 Part 1 of 4 To…

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Q: 39. F(s) = -2 2 5²-1 1 S-1 1 S+1

A: Solution- Given function is, F(s)=2s2-12s2-1=1s-1-1s+1 We know L-1(1s-1)=et L-1(1s+1)=e-t

Q: Find a unit vector in the direction in which f(x, y, z) = 2 y² increases most rapidly at P(1,2,-2),…

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Q: When converted to an iterated integral, the following double integral is easier to evaluate in one…

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Q: The radius of a circular oil slick expands at a rate of 2 m/min. (a) How fast is the area of the oil…

A: Radius of a circular oil slick expands at a rate if 2 m/min That means  dr/dt = 2 m/min

Q: Which of the following is true of Select the correct answer below: 36 The integral converges to…

A: Definite integral

Q: Let f(x) and g(x) be continuous functions defined everywhere. Suppose the tangent line to the graph…

A: The tangent line to the graph of f(x) at x=4 is y = 1.2x-4 The value of f4 = 0 The tangent line to…

Q: Find a unit vector in the direction in which f(x, y) = 9x³y most rapidly at P(-1, 1), and find the…

A: Given f( x, y ) = 9x5y6

Q: (a) Find an equation of the tangent plane to the surface at the given point. x + y + z = 12, (3, 5,…

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Q: Assume that the demand for a product is given by x=(12-2p) ² where 0≤p ≤ 6. Use the elasticity of…

A: For the maximum revenue , elasticity will be equals to one  Let elasticity of demand denoted by EOD…

Q: Given that Vf(2, -13) = 2i- j, find the directional derivative of the function f at the point (2,…

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Q: Uranium-238 (U-238) has a half-life of 4.5 billion years. Geologists find a rock containing a…

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Q: Given that find the Laplace transform of C{√= cos(8t)} = √√cos(8t). L{cos(8t)} e-8/s √√8

A: ℒcos8tπt=e-8/ss

Q: Solve the initial value problem below for the Cauchy-Euler equation. ty"(t)- 10ty' (t) + 30y(t) = 0;…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the graph to state the absolute and local maximum and minimum values of the function. (Assume…

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Q: The base of a solid is a circular disk with radius 2. Parallel cross sections perpendicular to the…

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Q: y=0 www 17

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Q: Decide the following integration formula is correct. O yes O no S x² dx = x5 + c

A: Check Integral is correct

Q: Find the gradient of f at the indicated point. f(x, y) = sin x² + cos 3y; NOTE: Give your answer in…

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Q: 4 √16-x² 3 SS S 1 + -dz dy dx = -4 0 (Type an exact answer, using as needed.)

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Q: An object with an initial position of x(0)=5 has a velocity of v(t)= sin 2t. what is its position at…

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Q: Answer: Find the interval of convergence of Note: Give your answer in interval notation ………………………...…

A: The power series ∑n=0∞cnx-an converges if x-a<R where R denotes radius of convergence such that…

Q: 1. Express the triple integral ſſſ ƒ(x, y, z)dV as an iterated integral. E 2. Evaluate the iterated…

A: we have, x2+y2+z2=8  and z=x2+y2      z=2 x2+y2+z2=ρ2 8=ρ2 ρ=22 here,  0≤ρ≤22 and  z=ρcosϕ…

Q: -5- (0,2:6) (-2-3,0) (0-0) -5 0 -5- GREEN TREE EN (2.6-0-- VALPA 10

A: (x - h)2 + (y - k)2 = r2 where, center of circle : (h, k) radius of circle : r

Q: The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is…

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Q: Ife is the angle between a line through the origin and the positive x-axis then the area (cm²) of…

A: Given thatdθdt=510, A=9164θ-sin(4θ)We have to find the value dAdt at θ=π12

Q: Optimal Speed of a Truck A truck gets 600/x miles per gallon (mpg) when driven at a constant speed…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: Use a linear approximation (or differentials) to estimate the given number. (Use the linearization…

A: We have given the number 1/99. Since 100 is near integer of the value 99, choose the value a = 100…

Q: Use a computer algebra system to graph f and to find f' and f". Use graphs of these derivatives to…

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Q: Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's…

A: Given demand function  p = -0.0005x + 10  Given Cost function  C( x ) = 600 + 2x - 0.00003x2

Q: The quadratic function f(x) = a(x − h)² + k is in standard form. (a) The graph of f is a parabola…

A: Please see the below answer.

Q: Find the derivative of the function. y' 11 || 1-¹ (x - √1+x²) y = 7 tan X

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Q: Find the absolute extrema of f(x) =8x^3 +81x^2 -42x -8 on [-8,2]. If possible, using the first…

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