Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

Q: 1 Find the area onclosed by the Curve r=4-3 sin 0.

A: Area

Q: Find the generating function for this when n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5,…

A: Given :n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5, f(5) = 125. n=6 f(6) = 750To find : The…

Q: In the year 2000, the population of a small city was 43,000. The population grows at a rate of r(t)…

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Q: sec" /x dx 17. 2 5n Ans. 6

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.004q - 0.9q + 615. The…

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Q: The solid shown in fig 1 has two parallel bases. Plane BFHC forms a dihedral angle 50 degrees with…

A: Aim: To find the area at the midsection of the given figure…

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

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Q: (2xy+x^2+x^4)dx - (1+x^2)dy=0 the answer should be

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: 5. Differentiate with respect to x: SET A. 5e

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Q: The study of integrals in calculus is motivated by the problem of calculatin (a) the slope of a…

A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: Let A = 2. Find the eigenvalues of A 3.

A: Use eigen value concept

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

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Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: integration

Q: 2ln|x| + 3 ln|x + 1| – * - + C 5x2+11x+2 dx x(x+1)2 2ln|x| + 3 In|x + 1| ++C 4 2ln|x| + 3 ln|x + 1|…

A: Given: I=∫5x2+11x+2xx+12dx   As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C And…

Q: A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it…

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Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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Q: im Y cosx tZx 7x¢ with squeze thearem

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x %3D and…

A: Moment of inertia with respect to x-axis , Mx= ∫A y2 dA.

Q: 1. Find the angle between the following two vectors. and

A: The given vectors,  8,-5 and -9,-7

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = 3xy and above…

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Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: Given the linear differential equation: y'' - y = cos(x) - 5sin(2x) Find the general solution…

A: Solving

Q: 6. Determine. 2r - 3x 4x SET A.

A: I have stated the used formula in the solution

Q: H.W (5) Solve the following differential equations of (3x -6xy)dx+(-3x' -2y)dy 0

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Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (5t + 6)i + tj, 0sts1

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Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

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Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

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Q: dx 00 2 X х +4

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: 6) Find the SVD of the matrix by manually calculating U 4 11 14 A = 8 7 -2]

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Q: nvestigate the convergence of the following series. H.V 2n+5n 2) Σ-1 3n %3D1 1LJ!

A: We have to find out convergence

Q: Solve the logarithmic equation algebraically. Approximate the result to three decimal 8+ 7ln x = 14…

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Q: Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298…

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Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: Consider the following statements. 1-If B is a symmetric matrix of 9x9 so the elements b32 and bz3…

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Q: What is the range of the function y=f(x) =2sin 57 A [-3,7] B B [-7,-3] В © [-7,3] D D [3,7]

A: We have to find range of give function.

Q: y 3 y = V x 1 (1, 1) X = 8 y = X 2 4 6 8

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Q: 1. Find the particular solution of the differential equation that satisfies the initial conditions.…

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Q: For the function f(x) = - 2x-3, do the following. (A) Find the average value of f(x) on the interval…

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Q: Find the derivative of this function

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 4

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Q: cos x e) f(x)= e* х

A: Topic = Derivative

Q: Sing do Coso + Cose-2

A: LetI=∫sinθcos2θ+cosθ-2dθPut cosθ=uDifferentiate on both…

Q: If y=f(x) = - 3cos+) + 4 then what is the value of / 2 A) 7

A: