Compute the following.• Arc length of y = (1 + x)2 with 1 ≤ x ≤ 4.• Area of the surface of revolution generated by the curve x = 1/3 y3 when rotating it about the ~y-axis.

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A: To determine the following limit.

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A: Given that the marginal propensity to consume is

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A: Given that the region is bounded by the graphs of

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A: The given function is where d is diameter and length is L.Here, L=12 and d=22

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A: The integral will be ∫ab​1+4xcos2x​​​dx.Explanation:Steps and explanations are as follows:In case of…

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Q: Evaluate the integral or state that it diverges. Ĵ 0 (3v) 1+9v² 30 tan -dv

A: The given integral .The objective is to find the integral value.Formulas used:

Q: (5.) Let u(x, y) = ln(x² + y²) (a. (c. State the domain of u: Determine lim f(x, y) (x,y) →(1,0)…

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Q: 5 Similar to 8 ft wire page KX wire 326 : 83 11 ft > with different numbers. [use Calc.] ➜ 15 ft…

A: The given figure

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A: Given graph of the derivative of a function.We get critical numbers when the derivative of the…

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Q: The following series, e² + e¹ + 6 + 8 + e 10, expressed in sigma notation is: ✗1e2k. true false

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A: f(x)=A function y = f(x) is uniformly continuous at an open interval (a, b) if f(x) is continuous on…

Q: X y = y 77 225 471 877 3 1480 1.5 2 2.5 Paste the table into Desmos and fit the requested type of…

A: (a). Exponential function: The exponential function that best fits the data is :…

Q: Problem #2: Evaluate and determine whether the function is continuous at (0,0). Provide…

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A: Given Differential Equation is as follows Given Initial condition

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A: Given the wind-chill index is modeled by the

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Q: Use long division for the following calculations. Estimate your answer first. 456 16 987+28 843 ÷ 27…

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Q: Find the point, P, at which the line intersects the plane. x=8-10t, y=4+9t, z = -4 -3t; 10x +9y+…

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Q: 10. The function g(x) = x² = kx³ + 4x² - 5x +9 has a minimum when x = 2. Determine the value of k.

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Q: Please solve this vector calculus practice problem showing all the steps. Thanks!

A: Solution is done.Explanation:Approach to solving the question: Detailed explanation: Examples: Key…

Q: Please help evaluate each sum knowing that f(x) = x2, g(x) = 3x , & h(x) = 2/x

A: f(x) = x2, g(x) = 3x , & h(x) = 2/x

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Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Question explained below:Explanation:ANSWER :​​

Q: Calculus 2 Let A E RNXN be a symmetric, positive definite matrix and b E RN a vector. If x ERN,…

A: The integral Z(A, b) as a function of A and b is given by: Z(A,b)=e21​bTA−1b(2Π)Ndet(A−1)​ This…

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A: 6.4099 feet per secondExplanation:Step 1: Identify the measurements of the ladder Let x be the…

Q: f(t) = 2t2⁄3 + t5⁄3. Find the interval(s) where  f(t)  is increasing and Find the interval(s) where…

A: interval of increase (-inf, -4/5)U(0, inf)interval of decrease (-4/5 , 0)Explanation:hope it helps…

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A: The radius of a circle is increased from 3.00 to 3.02m.

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Q: (a) In e² = (b) elh3. (c) en √3 (²) e4 (d) In

A: (a)A=ln⁡e7Using property of logarithmloga⁡mn=nloga⁡m

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Q: Suppose that for a company manufacturing calculators, the cost and revenue equations (in dollars)…

A: Answer :: Rate of change in Cost :: 24,000 Rate of change in Revenue :: 3,18,400 Rate of change in…