. Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x = and y = 0 by revolving about the x-axis. 2

Q: Find L(te²t sin 3t)

A: Ltsin3t=2(3)s(s2+32)2               Ltsinat=2as(s2+a2)2               =6s(s2+9)2 Now,…

Q: O O O O It is reflected over the x-axis and shifted right three units. It is reflected over the…

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Q: dx ef. using rationalizing substitution. x1/2 + x2/3' Evaluate

A: We know that integration of xn is xn+1/n+1.   Here i attached the solution of this question.

Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

A: The area of a rectangle with length L and height H is given by A=L×H. We use chain rule , power rule…

Q: Sx [x²cox dx U. V x² Sax - S(α (x²) [ cond) dx dx x² (sinx) - -S 2x Sinx dx U. V. x² sinx - [2x…

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Q: 3. The Critical Point of y = xe-*

A: Answer :-  We have to find the critical point of y = xe-x

Q: a²z Find of z = In(xy) a²y

A: To find out the double partial derivative with respect to y

Q: A street light hangs 24 ft above the sidewalk. If a man 6 ft tall walks away from the light at the…

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Q: 2. Use polar coordinates to find the volume of the solid under the paraboloid z = x² + y² and above…

A: Let's find volume of solid by using polar coordinates.

Q: Prove 3. The auxiliary equation of the differential equation (D² - 6D+9)y = 0 falls under. your…

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Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

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Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

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Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y: cos X B…

A: Let's find.

Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: /Find the directional derivative of the function (f(x, y, z) = x + xcosz-ysinz+y), P₁(0,1,2). at…

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Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

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Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A: Using logarithmic function

Q: efv. Evaluate dx Use rationalizing substitution. A B 8 √e² - 2 - 2√2 Arctan — √e² - 2 + C e³ − 2 −…

A: Let's evaluate given integral by using rationalizing substitution.

Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…

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Q: Suppose that it + [[ f(x, y)dA - 26 and ₂⁹(2, 3)dA R R (A) The value of [kf(x, y) + g(x, y)]dA is […

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Q: Question 8 Using Simpson's method 2 √ ²x³ dx for n = 4 is equal to

A: Simpsons rule

Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

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Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: a cylinder is inscribed in a sphere of radius a,solve for the maximum volume.complete solution.

A: Given problem:- A cylinder is inscribed in a sphere of radius a,solve for the maximum volume

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

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Q: 2 S²3 (x²-3x+18) 9x-X³

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Q: y = x²sin (3x)

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Q: 8. Find the area between y = sinx cosx and y = sinx, over the interval 0 <x<T

A: Given y=sinx cosx &amp; y=sinx between the limits x=o to x=πTo find area between two curves:

Q: So .x² dx (2x²+2x+1)²

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Q: Calculate the points of intersection of the curves x² = 4y and bre yavas r3 099wied biloa 9d1 to 9…

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Q: The Maximum point of y = 9-x² x²-4

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Q: At what points does the helix r(t) = (sin(t), cos(t), t) intersect the sphere x² + y² + z² = 82?…

A: This question can be solved by putting x=sint, y=cost, z=t in the equation of sphere to obtain the…

Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

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Q: 1. S In(x+2) 2x+4 dx

A: Given,∫lnx+22x+4dx

Q: dx 2 X - 25

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Q: Write TRUE or FALSE before each statement. Solve+Q=4. independent variable. the above differential…

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: Numerical Integration: c2 S 1 √x 1. =dx

A: The integral is  ∫02 1xdx

Q: 19. Find the volume of the solid that results when the region enclosed by = 2y, y = 2, y = 3 and x =…

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Q: The reverse order of 4 So Say ex² dxdy is equal to e-1 8e None of them

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Q: Question 2 Given a differential equation as d²y dy 2². - -3x- +3y=0. dx² dx By using substitution of…

A: Let's solve diffrential equation by using substitution x=e^t  or t=ln(x).

Q: Find the measures of the angles of the triangle whose vertices are A=(-2,0), B=(3,3), and C=(1,-1).…

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Q: 7. Which of the following is the differential equation satisfied by the given by the particular…

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Q: Find L-1 (5² 7². 2s+3 s²+4s+13

A: To find the inverse laplace.L-12s+3s2+4s+13

Q: Evaluate: L{cos(3+2t)} s cos3+2sin3 A s² +4 S (B (s+3)² - 4 S (s+3)² +4 s cos32sin3 s² +4 (c) (D)

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Q: If = (6,-5) and a = (-2,6), find |2c +3.5d|. O √146 O 16 O 2√73 O 5√11

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Q: Q3/Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: Two small planes approach an airport, one flying due west at 100 mi/hr and the other flying due…

A: Solution is here

Q: Q3/ Solve the following. Choose two only. 1. lim x lnx³ X-0 2. lim x sin(1/x) 818 ex+2x 3. lim 818…

A: According to the question, we will calculate the limits of any two subparts.

Q: (D5+ D4-7D3³ - 11D²8D-12)y = 0

A: