Evaluate dw dt OA. -9 OB. 5 O C. 11 O D. 7 at t= 1 for the function w(x,y) = x² - y² + 9x; x = cos t, y = sin t. 2t

Q: - 49 -dx = X (Type an expression using x as the variable.)

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Q: The temperature in a hot tub is 103° and the room temperature is 75°. The water cools to 90° in 10…

A: Here we apply the Newton's law of cooling

Q: Average Cost for Producing MP3s The average cost (in dollars) incurred by a media company each week…

A: Here is the solution:

Q: mine the average rate of change of f(x) = x³. - x over the interval 1 ≤x≤ 3.

A: We will find the required.

Q: x ». Let g(t) be the function whose graph is given below. Let G(x) = g(t) dt, 0 ≤ x ≤ 5. Where does…

A: Given: Gx = ∫0xg(t)dt   , 0≤x≤5 To find: The point of maximum and minimum of G(x) and maximum ,…

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: Find the area of the region cut from the first quadrant by the curve r=8(3- sin 20)

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: A function y=f(x) is said to be increasing in the interval (a,b) if for every x∈(a,b), f'(x)>0.…

Q: > Let f(x) be the function shown in the graph below. Click on the graph to enlarge it. Determine the…

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Q: Find the average value of f(x,y) = sin (x + y) over 0≤x≤/3, 0≤ y ≤5/3 0 ≤x≤2/3,0 ≤ y ≤7π/6 a. the…

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Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: 2. Find the derivatives of each of the following functions. You do not need to simplify your answer.…

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Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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Q: The​ short-term demand for crude oil in Country A in 2008 can be approximated by q=f(p)=2,443,225p…

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Q: Question 18 ( Show that the equation has exactly one real solution. 207e+2023 In 24

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Q: Consider the function f(x) = 12x5 +75x¹ - 120x³ +1. For this function there are four important…

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 4 sin…

A: By using the double integration to find the area of the plane region  enclosed by the curves. y=sin…

Q: Q8 Find the slope at x = 2 on the graph of f(x) (a) -3 N/W (b) 3/3 (c) 3 4 = 3 (d) 0

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Q: This was incorrect

A: The given function is; f(x,y)=ln(x3+y3).

Q: - The function ƒ(x) = 2x³ − 33x² + 144x – 2 has two critical numbers. The smaller one is x = and the…

A: Please see the below picture for detailed solution.

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: We have to find the volume of the solid by rotating the region in the firs qudrant bounded by the…

Q: Let a = (3, 5, — 3) and b = (1,3,0). Find the projection of b onto a. proja b=

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Q: Determine an expression for the derivative of this function. (Do not simpli f(x) = (2x²-x)(√√x² - 1)

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Q: (a) Find the derivative. y = In(4x - dy dx (b) Find the derivative. y = ln ( 4x = dy dx 6) - 3 In(x)…

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Q: Solve the initial value problem for x as a function of t.. (t²-19t+90) dx dt x(t) = (Type an exact…

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Q: Find the surface area of revolution about the 3 y-axis of y = 10x over the interval 4 0 < x < Enter…

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Q: A student drew the graph of y = f (c), y = f' (x), y = g(r), and y = h(x). Unfortunately, they…

A: Find the graph of y=fx and y=f'x.

Q: The graph of y = f'(x) is shown. 10 9 -8- 7 6- 5 4 3 2 1 10-9-8-7-6 फं A -2 -3- -4 -5 -6 -7 -8 9 10…

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Q: Differentiate the function. f'(x) = f(x) = log₁0(x⁹ + 7)

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: Given:-  The solid obtained by rotating the region in the first quadrant bounded by the curv x = 0,…

Q: Solve the given differential equation. 3ydx - 3xdy + xdx = 2dx

A: 3ydx-3xdy+x9dx=2dxwe know ∫xndx=xn+1n+1+cd dx(yx)=xdy-ydxx2

Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

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Q: Differentiate the function. f'(x) = f(x) = In(cos(x))

A: The solution is shown below-

Q: Consider the graph below. Which of the following is the correct setup for the area of the shaded…

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Q: Find the arc length of the curve y = ln x - ²² on the interval [1,3].

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Q: Find the volume of the pyramid with base in the plane z = -10 and sides formed by the three planes y…

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Q: Evaluate the limit sin 5x lim 10 sin 2x

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Q: Find the limit. lim 0-0 cos(0) 1 sin (0)

A: Given limit limθ→0cosθ - 1sinθ

Q: Consider the function f(x) interval. = 1 on the interval [3, 9]. Find the average or mean slope of…

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Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 4) * I→∞

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Q: Use the washer method to determine the volume of the solid formed when the region bounded by y =…

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Q: Evaluate the limit using L'Hospital's rule if necessary x 5 7 lim (1+1)

A: To find the limit

Q: In which limits below can we use L'Hospital's Rule? 1- eª x+0 sin(6x) Olim lim I→∞ lim I→0 lim x →∞…

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Q: The perimeter of a rhombus is 68 inches and one of its diagonals measures 30 inches. Find the area…

A: Topic = Geometry

Q: A water well has an 8-inch diameter and is 180 feet deep. The water is 15 feet from the top of the…

A: Given: Pumping the well dry which is 8- inch in a diameter 180 feet deep for which the water is 15…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x², y = 0, and x = 1,…

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Q: Find the values of x, y and that correspond to the critical point of the function: z = f(x, y) = 4x²…

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Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A: If x=c is a critical point of the function f(x) if f(c) exists and if either f'(c) =0 or f'(c) does…

Q: The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer…

A: We have to find m'(-1) and n'(6) Where m(x)=f(x).g(x)        n(x)=g(x)/h(x)

Q: Use a differential to approximate. (Give your answer correct to 4 decimal places.) 4(3.98) (3.98)² +…

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