6- Find the volume of a solid, use the Cylindrical Shells method, which involves rotating the region enclosed by around the y-axis. y = 3x - x² and y = x.

Q: a. [8t7dt dx b. S sin x tanx C. d. S [ 26* dx 3d8 √8

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Q: a=i+3j 2k, and b=i-3j-k, and c = 2ī+j-k, then...

A: Given problem:- a = i + 3j − 2k b=i - 3j - k c= 2ì + j − k  Then find v= 3(a - 2b +5c).

Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (8y² − x² + 7) dy = 0 s exact. If…

A: Topic:- differential equations

Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: Evaluate the determinant of the given matrix by reducing the matrix to row-echelon form. 4 -4 16 A =…

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Q: A 200-g sample of a radioctive substance is placed in a chamber to be tested. After 3 h, 140 g of…

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Q: H.W: Given the following table find x3, fo Af₁,Af₂, A² fo j xj Afo A² fo 0 fo 30 A² fo 4 20 Af₁ 2 14…

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Q: An object moving in a straight line travels s(t) kilometers in t hours, where s(t) = 8t² + t. (a)…

A:

Q: A 200-g sample of a radioctive substance is placed in a chamber to be tested. After 3 h, 140 g of…

A:

Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x)= |x-1| In its domain. a.…

A:

Q: Given f(x): 5x² 6x +13, find f'(x) using the limit definition of the derivative. f'(x)=

A: Given problem:- Given f(x)= = 5x²-6x+13, find f'(x) using the limit definition of the derivative.

Q: (b) [x² x²9x8 – 12x4 + 4 dx 2

A: We need to solve integral.

Q: Create a table of values for the function and use the result to estimate the limit. Use a graphing…

A:

Q: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Solve 2 cos² (x) - 3 cos(x) + 1 = 0 for all solutions 0 ≤ x < 2π X = Give your answers as a list…

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Q: Find f(t). ℒ−1{(2s + 7) / (s2 + 8s + 65)}

A:

Q: The area bounded by the parabola y² = 4x and the line y = 2x - 4 is equal to {A} 7 sq. units {B} 9…

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Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

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Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

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Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

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Q: Evaluate lim 00 0-1/1/201 O None of the choices ¹ 0-1/201 O 14 tan z 1 x cos x

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Q: Write the first five terms of the sequence, give the exact answer: too n n+7 n=1 Determine whether…

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Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

A:

Q: 3. Algebraically solve the equation 2(C₂) ==(n+1²3) 5

A: Given 2(C2n)=15P3n+1

Q: lim h→0 f(1+h)-f(1) B)-f(1) h 5/14 Correct where f(x) = 9x² + x - 4

A:

Q: c) What is the loss the company incurs when it tries to maximize sales (that is, produce the maximum…

A: Find out the loss the company when it tries to maximize the sales.

Q: What is the exponential growth rate change of an investment that has a b=1.92?

A:

Q: 2x+5 x-3' to y = = ( 2. For the rational function y = transformations compared write the equation in…

A: We have to solve given Questions.

Q: Find the value(s) of k that makes the given function continuous. (-x+2 if x < k f(x) = 4x + 3 if k ≤…

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Q: As shown in the required readings or videos use a power series to find a general solution to Airy's…

A: Given : Airy Equation : y"+xy=0

Q: Solve the following quadratic equations (if they have solutions) a. 15x²0 = b. 2x² +9=0 c. x² - 4x +…

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Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: lim (3x6) sin = 818…

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Q: Find F(s). ℒ{et sin 3t}

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Q: Evaluate the following sums: a.--22√k+2 b.Σ o(x + 2i)2 3

A:

Q: 6. The rational function f(x) = + k is transformed to g(x) = -5f(x+3)-1. Which row in the table x-2…

A: We have to find the solutions

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: Prove that if i and k are relatively prime positive integers, for every positive integer l the…

A: Concept: Number theory: Number theory is an area of mathematics that aids in the study of the set of…

Q: Use a graphing utility to graph the equation. Use a standard setting. y = x2 + x − 12   Approximate…

A: The given function y=x2+x-12

Q: Let f(x)= Select the correct description of the one-sided limits of f at x = 0. Choose 1 answer: lim…

A: Above question is solved.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

Q: Find the arc length of y = 26² + O 7/12 pi O 17/12 O 7/2 pi O Not in the choices O 17/2 2+2 for for…

A: To find the arc length of y=x36+12x for 1≤x≤2.

Q: Let f(x) √5 + 2. Using the definition of derivative at a point, a. enter the expression needed to…

A: f'(x) = limh→0f(x+h)-f(x)h ( first principle derivative)f(x) = 5x+2Apply first principle derivative…

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A: We have to find the series is convergent or not and find the sum also.

Q: Consider the basic macroeconomic model: Y=C+I and C = a + by where Y is GDP, C is consumtion and I…

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Q: 18. The solution of the differential equation 2xy = x² + 3y² when y(1) = 3 is dx

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Q: y" - y = xe*, y(0) = 2, y'(0) = 1

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Q: T Express the surface area of the surface obtained by rotating the graph of y = 4 sin (x) for 0 ≤ x…

A: Recall: Surface area SA=∫ab2πy1+dydx2dx We have, y=4sin(x), a=0, b=π6

Q: 2- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = C

A: Given problem:- Find the equation of the tangent line to the curve 7xSin(3y) + 5y = 7 at y = 0

Q: 1. The rate of change and when 0,xo = 3 t= when =47 is proportional to When What is the value of t =…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…