Find the average value of y = x(x² + 1)² over the interval [0, 2]

Q: he surface area of the surface = (u cos v)i + (u sin v)j + (u)k, 0≤u ≤ 2 and

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Q: Find the indicated term of the sequence. The eleventh term of the arithmetic sequence-10, -14, -18,…

A: The arithmetic sequence is given byTo determine: The eleventh term of the arithmetic sequence.The…

Q: eliminate the parameter to find a rectangular equation for the plane curve defined by the parametric…

A: The objective of this question is to eliminate the parameter 't' from the given parametric equations…

Q: Determine the slope of the tangent line, then find the equation of the tangent line at t = -1. x =…

A: The given curve .The aim is to find the equation of the tangent line at .

Q: Name the quadrant in which the angle 0 lies. sin 0>0, cos 0 >0 The angle 0 lies in which quadrant? O…

A: Sin(theta)>0, cos(theta)>0

Q: Find the value or values of c that satisfy the equation C f(x) = 2x³-3x², [-2,3] f(b)-f(a) b-a =…

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Q: est rate (compounded each year) t years after opening with $P is given by A(t) = P (1 + 100/…

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Q: Current Attempt in Progress Evaluate the integral using an appropriate substitution. NOTE: Enter the…

A: The given integral is x3+5)3

Q: Find all holes of the following function. If a hole exists, write your answer as a coordinate point…

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Q: Walt goes for a 12-min walk. His pedometer shows his speed, v(t), in miles per hour, for 1-min…

A: 1 min interval

Q: Find the indicated value of the function f(x,y,z) = 4x - 5y² +8z³ - 7. f(4, -3,1) f(4, -3,1)=

A: Given,

Q: Express the Cartesian coordinates (-5√3,-5) in polar coordinates in at least two different ways.…

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Q: At the beginning of 2000 Mark's house was worth 222 thousand dollars and Randall's house was worth…

A: An exponential function is given by where,  are constants.

Q: 9.7c -0.025215 9,7,-0.025216 = 55-3 451 1108 - 2- ? 0.3

A: The given equation is

Q: 42. Find the work done by the force F = ei + (lnx)j + 3zk, where force is measured in newtons, in…

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Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

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Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: Let g(x)=x²+ex and let g²¹ be the inverse function a) I 3+e b1 ㅗ 3+3e c) 3+e

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Q: Suppose the temperature in degrees Celsius over a 10-hour period is given by T(t) = -t² + 5t +31. a)…

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Q: Evaluate the integral: fe²* sin 3xdx

A: The given integral .The aim is to evaluate the given integral.Formulas used:

Q: Find the binomial series for the function (1 – 6x)³. (1-6x)³ =

A: Function:

Q: The liquid base of an ice cream has an initial temperature of 85°C before it is placed in a freezer…

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Q: Find the average value of the function f(x) = x² – 23 on [0,3].

A: Find the average value of the function f(x)=x2−23 on [0,3]fave =1b−a∫abf(x)dx

Q: Question Find the derivative of the function Simplify your answer as much as possible. Provide your…

A: Givenf(x) = sec-1(3x²)

Q: Calculate and interpret ac ax ac ду C(x, y) = 18,000 +90x+ 20y. ac ac ax ду and = The marginal cost…

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Q: Dylan's body metabolizes caffeine at a rate of 12.8% per hour (so the amount of caffeine in Dylan's…

A: Given in the question, Dylan's body metabolizes caffeine at a rate of 12.8% per hour.

Q: 2) The figure shows a circle with radius 1 inscribed in the parabola y = x² Find the center of the…

A: The standard equation of a circle with a center  and radius r is Given that circle center on y axis…

Q: Let f(2)=√4z² + 6z Determine the derivative of f. f'(z) =

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Q: Problem 12. Using Logarithms to Solve.. a) How long will it take $1,000 to grow to $3,000 if the…

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Q: In ² x→∞ 9x Explain why we can use L'Hopital's Rule in this problem. Use it to find the limit.…

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Q: Find the exact value of the integral using formulas from geometry. 320k (1 + 2x)dx (1 + 2x)dx=…

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Q: Which of the following differential equation is a variable separable type of differential equation?…

A: A differential equation is said to be a variable separable type if it can be expressed in the…

Q: A box with a lid is to be made from a rectangular piece of cardboard 12 cm by 17 cm, as shown in the…

A: The equation that gives the volume of the box in terms of the length of is: To find the domain of…

Q: Use series to evaluate the limit. lim t-0 lim t-0 2-2 cost-t² 2-2 cost-t² 4 11 (Simplify your…

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Q: Given the graph of ƒ(t), let A₁ = 0.75, A2 = 5, and A3 = 2. Let F'(t) = f(t). A₁ -1 A. Evaluate [₁0…

A: Given the graph of .(A) To evaluate .(B) To find the total area from .(C) To find the intervals…

Q: Let r = -4sin 0. a. Find the length L of the graph of the polar equation. L = b. Find the area A of…

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Q: If a $500 loan is paid off with a payment of $615.72 after 1 year, what is the interest rate…

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Q: Find the indefinite integral. (Use C for the constant of integration.) /(- 800 (0.04p - 1)3) Now…

A: To solve:

Q: Determine r' (x) for r(x) = Provide your answer below: r'(x) = sin xex cos x using logarithmic…

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Q: Match the equivalent representations. I I I I I Submit Ⓒk² = 6 6² = k 26 = k Ⓒ 2¹ 2 = 6 = 2 Ⓒ 6² =…

A: 1) k2=62)62=k3)26=k4) 2k=65)k6=26)6k=2

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: f(x)=5x-2, a=1

Q: (2x-5)" Find the radius of convergence R and the interval of convergence I of the series 1 3 n³…

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Q: a) find dy and b) evlauate dy for the given value of x and dx y=esinx, x= pi, dx= -0.1

A: The given function is

Q: Need help

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Q: C(x, y) = 28,000 + 50x + 20y + 0.5xy. ac ac ax ду culate and interpret and Compute the marginal cost…

A: The cost to manufacture x bicycles and y tricycles is given by the function,We have to find and…

Q: Find the following for the vectors v = 11i +2j-10k and u = 5i + 12j. a. v•u, |v|, |u| b. the cosine…

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Q: System: 2x² - y² = 1 x + y = 2

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Q: Problem (g. f) (1) r|1|5|8| 12 f(x)|-2|8|2|12 x|5|2|1|3 g(x) |1|5|5|8 <TD

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Q: Consider the function f defined implicitly by: y² + In (xy) = 2. a) Find and sketch the tangent line…

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Q: A thin wire with the density function p(x, y, z) = 1 + x lying along the curve (t) = (2 cost)i + (2…

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