4. A solid is obtained by rotating about the x-axis. The curve is given to be as y = 3x2 – x³. Find the volume. %3D

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: ((- +3) dt 21.

A: the given integration,       ∫0245t3-34t2+25t dt

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Q: A curve is defined by the parametric equations x = sint, y = 1– cos t, 0 <t< 27.

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Q: Derive the Maclaurin series for f(x) = Cos x. Calculate the radius of convergence. What is the value…

A: The given function is : f(x)=cosx.

Q: (ii) Using the result of the derivative above and the fact that integration is the antiderivative…

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Q: Find the absolute makimum/minimum values of the function fCx)= x6-x) over the intenval 1Ex<5

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Q: v=(5,1,-2), w=(4,-4,3) find the angle of 0 between the vectors v and w.

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Q: 18 3. dz 36.

A: Topic = Integration

Q: The sum of two positive numbers is 16. Find two numbers such that the sum of the squares is a…

A: Given problem:- The sum of two positive numbers is 16. Find two numbers such that the sum of the…

Q: Let a = ci + jand b = 9i + 12j. Find c so that the angle petween a and b is=. Round your answers to…

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Q: Which of the following nuclides would be most likely to undergo beta decay? 135 130 125 Sn le 120…

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Q: Find an equation of the tangent plane to the surface at the given poin h(x, y) = In Vx2 + y?, (6, 8,…

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Q: pls show full solutions and clear   1. Show that the absolute value function is continuous at x =…

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Q: 1. Evaluate the indefinite integral, ſx² sinh x3 dx.

A: To evaluate the indefinite integral, ∫x2 sinh x3 dx.

Q: Direction: Find the first derivative of the following functions: 1. y = sin (2x)- cos (2x) 2. y =…

A: 3. y=tan(3x) cot(3x)4. y=cos x1+sin x6. y=xarcsinx+1-x2

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Q: Determine the area, in square units, bounded above by f(r) = x2 + 10x + 25 and g(x) = -x +1 and…

A: Topic = Area The area is 323.

Q: 43, 44, and 45 Evaluate the integral by changing to spherical coordinates. 43. xy dz dy dr

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: 5. Let f and g be the functions R →R given by 5- 3z if z<1 5-2r - if z1 f(z) = and g(z) - 6-2.…

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Q: Evaluate the iterates integrals II cos(s*)dtds

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 5) x²dx + y(x – 1)dy = 0 %3D

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Q: 9. cos(x-)

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Q: * | 2x)cx csch (2 sin -1 V1-4x²

A: The given integral,       ∫csch2sin-12xdx1-4x2

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Q: dy Use implicit differentiation to determine given the equation xy + e = sin(y). dx dy dx ||

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Q: A closed rectangular box with a volume of 1296ft is made from two kinds of materials. The top and…

A: answer is in next step

Q: 3. 8х' + 13 2. S 3 4x' + 8х + х + 2 2

A: integration

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Q: Use vectors to determine whether the points are collinear. (0, –2, –5), (10, 13, 15), (4, 4, 3) The…

A: The given points are,      0,-2,-5, 10, 13, 15, 4, 4, 3

Q: Applications of Integral calculus 3. The following curves bounds a certain area: y = 4x – x2

A: Area bounded by a curve y=f(x) on [a,b] is given by, A= ∫abydx

Q: Solve the differential equation with appropriate method. Finalize answer equated to y. y' = 2xy - x

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Q: d the vector component of v = 2i – j+ 3k along b = i+ 4j + 8k and the vector component of v…

A: We have to find the solution

Q: y= {(z) -4 -3 -2 -1 3 7

A: We have to find the points

Q: 22. Which of the following statements about the functions y = f(x) and y f(x) is true? A. If the…

A: Here, to find the correct statement for the functions y=f(x),y=1f(x)

Q: Solve the I.V.P: dy 1 = 6y°x; y (1) = dx 21 1 y = 24+3z2 1 3z2-24 1 y = 24-3z 1 24-3z? నా నా

A: To find solution of IVP

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Q: Use integration by part to obtain a formula for f x"e*dx and use it to find S x'e*dx. 3 5x

A: We have to find the integral

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

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Q: y =f(x) Enumerate all discontinuities of f(x) and identify their types. If a discontinuity is…

A: We have to find the discontinu points

Q: If g(2) = 3 and g'(2) = 1 and f(x) = [g(x)]°, find f'(2) %3D

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Q: 1 dx x2 V25 – x2

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 3. y = tan (3x)cot (3x)

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Q: Evaluate/Find the following integrals. dx 3. S. 3 1+ x

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Q: Find the derivative of the following functions from first principles. (i) x (ii) e (ii) log (x + 1)

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