Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not approximate any numbers in your answer.

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

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: test conerg ence and divergence h!

A: We can solve this as follows:

Q: Evaluate the double integral. 3r(1+ y²)¯ dA; R is the region in the first quadrant enclosed by y =…

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Q: 15. Evaluate L s-3 A) 2e e" +t- 61 +t-61° B) 2e " +1-6t -1– 61 C) 2e" +t-3t² D) 2e" +1-3t

A:

Q: (-1)"2"x" n=1

A: We will use ratio test to find radius of convergence.

Q: 23. y²dx + (xy – 1)dy = 0

A: Let's find.

Q: The measure of an angle 337.5 degrees is equivalent to ra 15 A 4 15n 8 13п 8 13п D 4. B.

A:

Q: _1. (2x – 3) dx А. —2 - _2. L (x³ + 2x) dx В. 0 _3. (x² – 2) dx С. 3 1 -

A: 1) ∫02(2x-3)dx2) ∫-11(x3+2x)dx3) ∫03(x2-2)dx

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

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Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

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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: sec'xdx

A:

Q: 46n Nhich of the following angle measure (in radians) is coterminal to an angle with measure 3…

A: Given problem:- Which of the following angle measure 46π/3 (in radians) is coterminal to an angle…

Q: A ball is kicked such that its height (h) can be represented by the equation h = - 16t2 + 64t + 9,…

A:

Q: - 4g° + 1000g, where R(g) is in dollars Suppose a product's revenue function is given by R(g) g is…

A:

Q: Given the expression below, y = ecos arc sec(ln(r |- determine y.

A: The derivative is given below

Q: 6. Vectors i and v are positioned at 115° to each other such that lü| = 15 and l0| = 7. Determine…

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Q: Let s(t) (2)a v(t) = Where does the velocity equal zero? [Hint: factor out the GCF] 4+12t2 36t be…

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Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

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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: 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: A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the…

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Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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Q: Question 5 Given the expression below, y = ecos" arcsec(ln(r 1)) determine y. Upload Choose a File

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Q: Question 4 Given the expression below, +. 4rab determine y". Upload Choose a File

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Q: In the year 2000, the population of a small city was 47,000. The population grows at a rate of r(t)…

A: For the following problem,

Q: Find the average value of the function f(x,y)=eˆ(y/x) over the region bounded by y=x, the x-axis and…

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Q: cos²(x) + 2cos²G) . cos³(x) - .dx

A: We have to find the integral.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: dy 2 + y = 0, y(0) = -3 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Regarding on the letter c, why is it equated to negative gamma?

A: c) The direction ratio of D→-C→ is -2, 5, -5 from part a. D→-C→ is normal to the required plane.…

Q: (-4)* 5k +1 k=1

A: We have to find if the series convergent or divergent.

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

A:

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

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

A:

Q: 1. The study of integrals in calculus is motivated by the problem of calculating (a) the slope of a…

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Q: Find the conservative vector field for the potential function by finding its gradie h(x, y, z) = 8x…

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Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: test conerg ence and clivergence h!

A:

Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

A:

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

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Q: 17. y dx — (х + бу?) dy %3D 0

A: To determine the solution of the given differential equation.

Q: Sing do Coso + Cose-2

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

Q: Suppose a product's revenue function is given by R(g) is units sold. 5g? + 500g, where R(g) is in…

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Q: Use continuity to evaluate the limit. 16 + Vx lim 16 + x

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Q: Evaluate the integral. (5 – 2t + 3t2) dt |

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Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows: