What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square root of 2 about the y axis?

Q: Employ trapezoidal rule to approximate value of the integral f() dx using the table given below. x|…

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Q: Solve the initial value problem y" – 6y' – 16y = 0, y(0) = a, y (0) = 8. Find a so that the solution…

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Q: Verify that the Mean Value Theorem (MVT) applies to the function f(x) = sin? x – cos x on the…

A: Mean Value theorem states that: f'(c)=f(b)-f(a)b-awhere f(x) is differentiable in (a,b).

Q: (1+ ye* + xye")dx + (xeª +2)dy = 0 C = xye + 2y + x C = xye" + 2y – x O Option 3 Option 2 C = xye –…

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Q: 4. Find the general equation of the plane passes through the points (3,2,1) and (3,1,–5), and is…

A: We have to find the plane equation

Q: Find dy/dx of the function. y=log2 x

A: To find derivative of given function.

Q: Find the points on the curve where there is a horizontal tangent line: x = 5cos(t) ; y = t3 - 3t2 +…

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Q: S(-uP +2u7 + uP)du No appropriate Match Question 6 S(-u° -2u7 - P)du Match the integral expression…

A: Solving the problem by finding the proper substitution.

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: en magnitude and the same direction as u. tion -8, 6, 4)

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Q: 2, 0 4 Evaluate a. lim f(x) X-4 b. lim f(x)

A: Given:        fx=x, x≤02, 0<x≤14-x2 , 1<x≤4-x+5, x>4

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Give all solutions of the nonlinear system of equations, including those with nonreal complex…

A: y= x2 +4x  ....(1)2x-y=-8 ......(2)2x -[x2+4x] =-82x -x2 -4x…

Q: Rand your an swer to the neullse thousandths. Whad yalve oftwll U:lil!1!

A: To find the value of t when the function value is 1111.

Q: tan (2x)dx, (Use 2 decimal Let x 0.49 and y = 1.9. Determine the value of C when you evaluate digit)

A: This question can be solved using the concept of ILATE.

Q: Find the area bounded by y = 2 - x squared and y = x

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Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

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Q: (a) Find dx

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Q: Find the centroid of the region bounded by the given curves: y = 1 + 2x2 ; y = 3 ; x = 0

A: To find the centroid of the region bounded by curves: y=1+2x2,y=3,x=0 The bounded region is:

Q: 4. Use §4.4 guideline to sketch the curve: y = x- 4x/3. A). Domain, Symmetry, Asymptotes,…

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Q: - y = V1 – sinx

A: Given,y=1-sinx3y=1-sin(x)13Differentiate w.r.t. x using chain…

Q: 5. For the Parametric curve x = a(t – sint), y = a(1 – cost) where 'a' is a constant. Find y d?y at…

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Q: Match the integral expression on the left to an equal expression on the right. Ssin(ax)sin(4x)dx +…

A: We know that; The trigonometric identitites; a). sinxsiny=12cosx-y-cosx+yb).…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: (x1, y1, z1) =(0, 0, 81)(x2, y2, z2) =(18, 18, 0)The parametric equations are given…

Q: Determine the value of C in on the antiderivative of F(x) = sin°(x)cos³(x) for x = 0.701 and y =…

A: Let's find.

Q: y(x) = x³ (2x – x²)

A: Given: yx=x232x-x2   As we know that; The Power law; ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: Determine the order and degree of the differential equation y' + y" = sinY O 1st order, 4th degree O…

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Q: Determine whether the planes are parallel, orthogonal, or neither. 2x - 10y - 2z = 5 4x - 20y – 4z =…

A: Solution is given below:

Q: If f(x, y) = 7xe5y + + 7y lnx, then is given by: 35e5y + 5/x 49e5y + 7/x 25e5y + 7/x 5లోbw + 7/a

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Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

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Q: A cylindrical can is to be made to hold 1 L of oil. Find the dimensions (in cms) that will minimize…

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Q: e component form of u + v given the lengths of u and v and the angles that u and v make with the…

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Q: find the derivative of the following functions using the basic differentiation rules. use the proper…

A: Part a,Given,            fx=14x

Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: y(2² – y² + 1)dæ – (x² – yf – 1)dy = 0

A: Option C)

Q: 32) Use the scalar triple product to determine whether the points A(1, 3, 2),  B(3, -1, 6),  C(5, 2,…

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

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: sec3x The integral of the given function dx is Atan3x cot 3x cot3x а. +C 9 b. – cot 3x, cot3x + C 3…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: The area of a sector of the circle with an arc measure of 45° and with a radius of 4 is A 16л 45° 4…

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Q: If f(x, y) = (17x - y)3, then is given by: af dy (17x (17 – ) 13 - 18 (17x 13 - - 13 Y)2 – ) 18 (17x…

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Q: af If f(x, y) 3x+7y (3x-7y) then is given by: 42y (3x–7y)² 21y (3x–7y)² 42y (3x-7y)2 21y (3x-7y)² -

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Q: (3k + 8)! Que Consider the series ) ak k3k QuE k=1 k=1 Que a) What is ak+1? Que Que Que: Ques ak+1…

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Q: f(x) =x' - 4x² +6x+5 is 1. Find the intervals in which the function increasing/decreasing. Also,…

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Q: Applications of Differential Equations A certain radioactive material is known to decay at a rate…

A: Let's find.

Q: 3. у'sec'xdx - (1- 2у'tanx)dy - 0

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Q: A table of values for f(x), g(x), f'(x), and g'(x) has been given. Ax) g(x) f'(x) | g'(x) 3 2 -5 1 2…

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Q: 10. y = cos In 7x6

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