Gilbert Strang video 'Min, Max and Second Derivative,

Q: e area of the blue region. It is the area under the curve. y 10 8 6 4 2 y = 3x+1 y = 6-x X 1 2 3 4 5…

A: The graph of the function is given.The aim is to find the area of the blue region.

Q: 17. What are the dimensions of the right circular cylinder of greatest volume that can be inscribed…

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Q: Solve the initial value problem 8y" - 2y' - y = 0, subject to y(0) = -0.2, y'(0) = -0.325.

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Q: he table gives the values of a function obtained from an experiment. Use them to estimate f(x) dx…

A: Consider the given table in the question.Given that n = 3△x=b-an"…

Q: (11,20) (11,20) Show that (40) fdx+ gdy = f(4,1) 24x²y³dx + 40y^³dy is independent of path: J(4,10)…

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Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A: Given,a(t)=t+4v(0)= 70=<t=<10

Q: If the marginal revenue for ski gloves is R'(x) = -0.5x + 55 and R(0) = 0, find the revenue…

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Q: dr Evaluate the integral: 2² (A) Which trig substitution is correct for this integral? Or=2 sin(0)…

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Q: Use the table of values to find lower and upper estimates of 10 [to f(x) dx. Assume that f is a…

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Q: f(x) = −x+10 g(x) = x² − x − 11

A: Given that the function

Q: 27. Maximize z = 5x + 8y subject to x ≥ 0, 2x + y ≤ 8, and x - 3y = -3. of flare

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Q: (– ²/6) has exactly one point of inflection with a positive x-coordinate. What is the x-coordinate…

A: The given function is .The aim is to find the point of inflection.Definition:If  is an inflection…

Q: The function s= -1³ 31²-31, 0sts 4, gives the position of a body moving on a coordinate line, with s…

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Q: Find (+72+6) dz + C

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Q: Find the area of the shaded region. r² = sin(20) P.

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Q: Two cylinders are given. The larger cylinder is a dilation of the smaller cylinder. Part A:…

A: Smaller length = 2mLarger length = 9mVolume of the smaller cylinder = 24 pi m3

Q: 3 fff Sayz dv= - S₁² S₁² ² 8zyz dz dz dy 2

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Q: Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate…

A: We have to find the number of calculators produced from the beginning of the third week to the end…

Q: The function y(x) saifies the following equation: Find an expression for dy dx 5 x² + 3xy +…

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Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

A: Given that the polar curve

Q: Use implicit differentiation to find the equation of the tangent line to the function defined…

A: The given equation is; 6x2+2x4y5=8Point (-1,1)

Q: Sketch the graph of the function shown below. From the graph, find its domain and range. |xif -3<x<0…

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Q: 3. Evaluate the integrals. a. b. /4 5*1*4 (sec (1))² dt [²7/x dx baxax 8x dx

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Q: 8. p-series below: (a) n=1 Use this fact to find the sum of each series below. (You may express your…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the tangent plane and normal line to In X 2y = z²(x-2y) + 3z +3 at (4, 2, -1).

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Q: For answer in part "E", is the answer 1/2 ln| sqrt(x^2+4/x^2) - 2/x |+C or 1/2 ln| sqrt(x^2+4) / x^2…

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Q: Evaluate the integral. 3 f(x) dx where f(x) =26-x² if -4 ≤ x ≤ 0 if 0 < x≤ 3

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Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A: Consider the given marginal-demand function,

Q: Express your answer as a polynomial in standard form. f(x) = -3x + 5 g(x) = x² + 2x + 15 Find:…

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Q: The equation z = x² + y² - 2x is given in Cartesian coordinates. Convert the equation to cylindrical…

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Q: 13. For the following limits, verify that direct substitution yields an indeterminate form. Then use…

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Q: L³₂x³dx -2 2 1 x+0.5 dx

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 4n²+3…

A: The given series By Root Test If L&lt;1 then series convergent If L&gt;1 then series divergent If…

Q: (a) The graph in the figure given below is made of line segments joined end to end. At which points…

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Q: The point(s) is/are (Type an ordered pair. Use a comma to separate answers as neeeded.)

A: Given that the graph with tangent line parallel to y=3x+1 we have to find the point is/are?

Q: Given that f (t) = t² - t - 5 represents the rate at which air is escaping from a balloon in liters…

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Q: Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = -1, v(0) = -7,…

A: Given that u and v are function of x that are differentiable at x=0At  To find:we have to find the…

Q: 6. 14 ) Consider both geometric series below. 3 SA = 00 Σ n=1 5n and SB = M8 n=0 3 5n Both SA and SB…

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Q: Find the difference quotient of f; that is, find f(x) = 3x² - 4x + 4 f(x+h)-f(x) h h#0, for the…

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Q: Find the cube roots of 125i. (Enter your answers as a comma separated list.) Sketch these roots in…

A: The given complex number is By De Morive's theorem The nth root of a complex number is

Q: Starting with an initial value of P(0) = 50, the population of a prairie dog community grows at a…

A: The growth rate of population of prairie dog community is P(0)=50

Q: Consider the indefinite integral ax + b + where Then the integrand decomposes into the form C d a =…

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = 6t², y = 4t³,…

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Q: 6. Σ. 1 n=1 1 ηγη2 +1 n

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

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Q: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

A: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

Q: Evaluate the following limits algebraically. 1. lim x---> -3         {-2x + 4; x -3 2. lim x--->…

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Q: To check for the result, you have to prove that + C] = 8⁹. + sec²0. d 1 10 de Evaluate the left side…

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Q: Find the area under the curve y = 9x5 over the interval [0, 2]

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Q: Suppose that we're making and selling some widget and the profit (in dollars) when making a widgets…

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