Use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y = 1 x21 y = 0, x = 4, x = 9

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) [0, 12] r 2 X…

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Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x³ - 18x²…

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Q: d²y dx² dy dx -+ 2y = cos (e-x)

A: The given differential equation is;  d2y/dx2-3dy/dx+2y=cos(e-x).

Q: Determine dy/dx y = (In 2x) - (ln(3x + 1)) 1 3x²+x 3x 1 None of the choices 1 3x²-x

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Q: Test the following series for convergence or divergence. State the test you are using and show all…

A: We need to check whether the given series diverges or converges.

Q: Bonus ( Show that given R: x € [0,1] Ay € [0,2] [[3x²yexydy dx = 6

A: See this solution in below

Q: Question 3 For the function below, how many regions are at least needed to facilitate the tracing of…

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Q: S(x + ex+1) dx 0 2. Sx5¹2 (x³ + x² - 7) dx 0 2x + 1 3. dx 2 0 e

A: Topic = Integration

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B. cos…

A: According to bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: What is the volume generated by revolving about the x-axis the region enclosed by the graphs of y =…

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Q: 1. Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2. 2. Find the length of the r(t)= , 1 ≤ t ≤ 5…

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Q: ind area bounded by y = 0, y =√x-x² using double integration.

A: We have to find area of given region.

Q: Evaluate x+1 S ex x² dx O e.e= + C O-e e + C O e e + C e = + C O

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Q: Q6A)If y=sin-¹ find Zxy.

A: partial derivative

Q: Find an equation of the tangent line to the graph of y = x³ – 3x – 1 at the point (2, 1). 09x - 2y -…

A: 1.y=x3-3x-1 at the point (2,1)2.y=logx2e

Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

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Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.…

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Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: Given

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: Given

Q: sin20 B)Evaluate the integrals: i) f/20 rdrde ii) f/2/2fix z² siny dz dy dx. sinx tt)

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Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

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Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 2. 2h(3)+g[f(-2)]…

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Q: Solve the differential equation: dx dy + x = e-y.sec²y

A: Here we have to solve the differential equation.

Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Given, f(x) =(2x-3) g(x) = -4x2+9 = 9-4x2 = (3)2-(2x)2 = (3-2x)(3+2x)  h(x) = 4x2-12x+9 =…

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: -(x²+y) dx x+siny B)Solve differential equation =

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Q: Let f be a function with continuous second partial derivatives and define: z = f (2x³y - y₁y³) if…

A: z= f(2x3y-y,y5) ,  u= 2x3y-y, w= y5   And zy= (2x3-1)fu+5y4fw  Find zyx

Q: Consider the following sequence x₁ = √₁, x₂ = √1 + √I, x3 = √1+√₁+√₁ Evaluate lim xn (No credit for…

A: The given sequence,x1=1, x2=1+1, x3=1+1+1

Q: 1. Find each of the following derivatives. d a. dx (4 sinx) b. [ln (2x4 - 3x)]

A: We have to find derivative of given function.

Q: t=sin³x B) [2 sintdt cos(sin 2x)sin 2x dx- A) sintdt D) [ 2 cos tdt →? c) fcos tdt E) fcos 2tdt 4.…

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Q: Fill in the blanks: 2² + 1 The equation describes an ellipse. The volume of the solid obtained by…

A: We need to find volume.

Q: B)Is w = Zez analytical function or not?

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Q: Evaluate the integral. 11 sec 40 tan ²0 do 11 sec 40 tan ²0 d0 =

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Q: consider the function f, such that f(x) = (ax + 3) * e*. If the slope of the tangent line to the…

A: Topic = Derivative

Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Find f'(0) if f(x) = a; a, b, c, d constant bc-ad O d² ad-bc (c+d)² ad-bc d² ad+bc d²

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Q: O- - 1 2x (In x)2

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

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Q: 8. 9. A) 1−sinx Ĵ (COSX + 1 COS X+X 2(cosx+x)2 E) ·x)³ dx = ? 1+tan²a (2 + tana)² -+C B) +C D)…

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Q: Question 10 Given z = (e-22) (sin y), find 92 O-2e-2 O-2 e 2 (sin y) + e-2 (cos y) O-2e-2 (sin y) -2…

A: We have to find derivative of given term.

Q: A manufacture has been selling 1600 television sets a week at $540 each. A market survey indicates…

A: (a) Here x is the number of television sets sold per week and p(x) is the corresponding price in…

Q: Assume that f is continuous on the set of real numbers. Find a and b given that cb 3 f(a)da - [³…

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Q: Find the area between the curve f(x) = x2 +11 and the x-axis from x = 3 to x = 7. The area is square…

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Q: The area enclosed by the two curves y = x² - 4 and y = x - 4 is given by. a. f(x-x²) dx b. (x²-x) dx…

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Q: B)Solve differential equation dx = -(x²+y) x+siny

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Q: d²y dx² 2 (2x-3)² Find y = O O d²y dx² d²y dx² d²y dx² O d'y dx² = = = = 12 (2x-3)¹ -12 (2x-3)4 48…

A: Given