Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation and fractions where needed. Enter the symbol o if the integral does not converge.) dx (x + 1)3

Q: Evaluate the indicated partial derivatives. z = 6a?y – 4a°y dz dz ду

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) withf,(1024, 1024) = 5 and…

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Q: Evaluate the definite integral. sin(3t)dt

A: I=∫0π3 sin(3t) dt  =-cos(3t)30π3  =-13 cos3π3-cos0

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Q: H.W: Use the comparison test to determine the following series converge or diverge: 1 3" +5 n=1

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

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Q: Find the Cartesian coordinates of the given point. O 1) (0, 1) 2) (1, 0) 3) (0, -1) 4) (-1, 0)

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Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: Let F = and C is the closed curve formed by y=x^2 and y=8-x^2, oriented counterclockwise. Use…

A: Using greens theorem

Q: A parametric curve is given by the equations: x (t) = 3 – t, y (t) = 2t, 0 <t < 3. After eliminating…

A: The given parametric curve is  x(t) = 3-t, y(t) =2t,   0≤t≤3 Here,  parameter is t.   We have to…

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: 15r If F(r) = and o is the surface (r – 3)? + y +z? = 49 oriented outwards, what is the value of F n…

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Q: 10. Given two points P1(0,2,-1) and P2(2,0,-1), find the perpendicular distance from the point P3(3,…

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Q: The traffic flow rate past a certain point on a highway is q(t) = 1300 + 2200t – 390,² where t is in…

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Q: How many times will you use double angle identities to solve the integral of (sinx)^2*(cosx)^2dx?…

A: ∫ sin2x cos2xdx

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Q: 00 1 dx x(Inx)2

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Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: - If g(x) 1 dt , find g'(2). 4 +t

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Q: uilding that is 225 feet tall casts a shadow of various lengths as the day goes by. An angle of…

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Q: Current Attempt in Progress Use Green's Theorem to evaluate the integral. Assume that the curve C'is…

A: Using greens theorem

Q: answer

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Q: Evaluate F. dr. F(x, y) = 7xi + 4yj C: r(t) = ti + V4 - tj, -1 sts

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Q: Find absolute maximum & absolute minimum f define on C0, 2]

A: maxima minima

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

A: Here we have to verify the Green's theorem.

Q: The derivative of p(t) = e'n(t)+4t² is given by which of the following? Op' (t) =D 글 + 8t Op'(t) =…

A: derivative of p(t) is p'(t)=ddtelnt+4t2

Q: Trigonometric

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Q: "he graph of x(t) = t+ cos t, y(t) =t+ sin t, 0 <t< 2n is shown belov 6 Compute the slope of this…

A: Topic :- application of derivatives  Note :- as per our guideline if more than one question uploaded…

Q: what is the domain and range of f(x, y, z) = x + ln y + cos z (please explain)

A: The given function is:f(x, y, z) = x +lny +cos z x is defined for all real numbers. So The domain of…

Q: 16 Find the constants a, b, c, d, e for the ellipse r = 6+2cos0

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Q: MP USING TOOLS Use a fraction or a mixed number to represent the tiT on a number line. Let 0…

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Q: 7) Determine the total area bounded between the function y = 1 – x between 1 and 1. -

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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Q: latch the vector field with its graph. F(x, y) = yi -6 5 5 -5+

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Q: n-1 (-3)' is convergent or divergent. If it's convergent, b) Determine whether the series 4" n=1…

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Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

Q: Sketch the region enclosed by Y 6x and y = 9x". Find the area of the region.

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Q: Find the limits. If you use L'Hopitals Rule, make sure to justify why you can use it. 1- cos(2r) lim

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Q: Evaluate CF dralong the line segment C from P to Q. F= x j; P(3,2), Q(3,8) SCF dr- i

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