Find the components of the vector with magnitude 5 and direction θ = 2π/3

Q: rectangle. y = 2/x, y = 4/x², x = 6 y y 35 30 25 -1 20 -2 15 -3 10 5 1 2 4 6 -5- y 5- 2 4 4 -2 3 -4 ...

A: Given problem:- Sketch the region enclosed by the given curves. Decide whether to integrate with res...

Q: Find the complete solution for the DEs.

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Q: dy Find using implicit differentiation, for the equation æ4 + yt = 7 is dæ O O O

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Q: Glven A = and B=. Determine the components, magnitude, direction angles of the vector B – 2A. Sketch...

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Q: 2х dx 1. x-2)²(x+ 2) |

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 10j as ...

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Q: Let f(r) = a and for each real number n > 1, define the function In(x) = 1 – (i) Find the area A, bo...

A: Two function are givenfx=x2gnx=1-1-xn     where n≥1.

Q: Decide whether the integral is improper. ** sin(x) dx 60 + x2 -00 O proper O improper Explain your r...

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Q: 6. S sin2xdr sin'r-4

A: We will use partial fraction to solve th integration after substitution. Which is as follows 

Q: 5. Simplify e3y + In y.

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Q: SOLVE USING: TECHNIQUES OF INTEGRATION: TRANSFORMATION BY TRIGONOMETRIC OR IDENTITIES AND INTEGRATIO...

A: First we let x=3/4y then put tanx=t then using t7 =t5 (t2 +1) -t3 (t2 +1) +t(t2 +1) -t

Q: (r + 3}* , ly-1} _ 1 16 4 1.

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Q: What is the general solution to the differential equation y[1 – xy tan(xy)]dx – x[1+ xy tan(xy)]dy =...

A: Put yx=v and solve it. 

Q: ; find value of matrix A eigen -2 A = 2. 2.

A: To find the eigen value of the given matrix A , we have to evaluate the determinant of A-λI and then...

Q: Sz2 - 7z + 1, z<7 8-z, z 7 Evaluate the following limits for h(z) = and Justify your answer. (1) lim...

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Q: y³e-2y dy

A: Given :∫y3e-2ydy

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: We will find the general term of the given sequence and then determine whether the sequence is conve...

Q: If f (x) =2r3+6x- 2, then what is f'(1)? %3D

A: We know that; The Sum/difference rule; f±g'=f'±g' The Power law; ddxxn=nxn-1 And c·f'=c·f' ; where c...

Q: Find the integral. 12 dt 4+3 A) (4+t)3/4 + C B. t (4 + t3/4 + C B - (4+t4 c 9(4

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Q: 19) Find [sin( x9+ 9x) ]' = _by Chain Rule A) 9x8sin ( x9+ 9x) C) 9(x8+1) cos x 19) B) -9 x sin ( x9...

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Q: What is the general solution to the differential equation ydx - ( x - sqrt(x² + y² )dy = 0?

A: Let's find. 

Q: 7/3 x tan (x) dx 2

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Q: Let a = ci + jand b = 6i + 30j. Find c so that a and b are orthogonal. c = i

A: The vectors are given by a = ci+j b = 6i+30j Condition for orthogonal vectors:  a·b = 0 To evaluate:...

Q: The number of bacteria in a culture is growing at a rate of 2500e2t/5 per unit time t. Find the numb...

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Q: (a) Find the cost and revenue if the company produces 500 units. Does the company make a profit? Wha...

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Q: Evaluate the Integral / tanh (u) du .

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Q: Find the area of the region included between the parabolas y? = 4(p + 1)(x +p+ 1), and y? = 4(p² + 1...

A: Here we have to find the area of the region bounded by the two parabolas.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (7x4 + 6)° dx...

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Q: Find lower bound for f(n) = 5n².

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Q: Find the area of the region between the parabola y = 9 - x² and the x-axis. Round your answer to thr...

A: We can find the area as follows:

Q: e2x dx 10. V1+e2x

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Q: (3x² + 1 +) dx 2х2

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Q: show complete solution and the sketch of the graph. Solve for the volume of the solid generated by r...

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Q: 4Vx + 2xVxdx X

A: ∫xn dx = xn+1n+1+C ∫af(x) dx = a∫f(x) dx

Q: 1) An equilateral triangular plate with 6m side is submerged vertically in a tank of water so that i...

A: Here, the top surface of the triangle plate is 2m  below the free surface of the water. Therefore, ...

Q: 2x2 + 1 dx 2. ") (x - 1)(x - 2)(x – 3)

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Q: State the trigonometric substitution you would use to find the indefinite integral. Do not integrate...

A: We have to find substitution of x

Q: Question 1 Find the indefinite integral of F (1) = / te*dr. A 28 e to the power of 4 t squared end e...

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Q: ution 1- u? cos x and dx 1+ u? grand to a rational function of u, and t al. If you have a CAS, use i...

A: We have to find the indefinite integral according to the given information

Q: 1/V3 dx 1+4x2

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Q: Which of the following three improper integrals is/are convergent? 1 +o∞ (1) S™* sin x dæ (II) S"™ S...

A: We have to find these integrals are convergent or divergent. 

Q: (x² – 1)*dx

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Q: S cos³y sin³y dy 3.

A: Given,            ∫cos3ysin3ydy

Q: 7 > k(2k + 1) с. k=1 7 2 7 k3 d. 4 k=1 k е. k=1

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Q: Integrate Intergrate 21x/ with recpect to X mtegrate X- 28 with respect to X

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Q: (x² - x') 6. Reciprocal Substitution -dx 3

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Q: x'dx 1. Integration by Parts f Vx4-5 dx 2. Algebraic Substitution f (x+2)vx+1 3. Trigonometric Subst...

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Q: II. Solve the following problems. Find the equation of an ellipse with center at (-2,2), a vertex at...

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Q: Sx² – 4x + 1, < 4 15-a, x 2 4 Evaluate the following limits for h(x)= and Justify your answer. %3D (...

A: This is a problem related to limit of the function. Function is called as continuous if it's right h...

Q: 2/3 over the interval sxs about the x-axis. Find the volume of the solid generated by revolving the ...

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