Exercise 7. GREEN'S THEOREM Use Green's theorem to calculate fo F R. All curves are oriented counterclockwise. (c) F (22 + y?)i+ (x2 – y?)j, C ellipse 4x² + y? = 16.

Q: Use the properties of natural logarithms to simplify the function. f(x) = ln(x/4)+ln(4)

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Q: Evaluate dw using the given information. 5x? + 4y? w = -; x= - 5, y= 3, z = 1, dx= 0.01, dy = - 0.08...

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Q: Let the demand function for a product be given by the function D(q) = – 1.55g + 300, whe items in de...

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Q: In the system of constant. For w ехас exactly one dist

A: Concept:ax2 + bx + c = 0can have only one solution when,when the discriminant is zero.b2-4ac = 0b2 =...

Q: Set up an integral that represents the arc length of the function y = 4a4 + 5x from the point (0,0) ...

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Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 3 3

A: To estimate the integral ∫025x2dx with n=4. Formula used: ∫abfxdx ≈Δ x3fx0+4fx1+2fx2+4fx3+…+4fxn-2+f...

Q: Find the value of a that will make the function continuous at every real number. x*, f(x) = {ax? + a...

A: We have to find the value of a that will make the function continuous at every real number.         ...

Q: Which of the following is/are true of f (x) = x²(x + 3)²? %3D

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Q: dy A-Find of the following: dx tan(5u) (1 + 2u)³ , u x. sin(x).csc(x) y = U = e4u

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Q: Evaluate the integral by first performing long division on the integrand and then writing the proper...

A: Given problem:- Evaluate the integral by first performing long division on the integrand and then wr...

Q: Find the time functions for each of the following Laplace transforms using partial-fraction xpansion...

A: As per our guideline, we are advised to solve first 3 subparts of the question . So please ask other...

Q: Estimate the area of the curve y= from r = 0 to r = 3 by using 6 rectangles and right end-points, R6...

A: area and right end sum

Q: 2. y(x? + y? – 1)dx + x(x² + y² + 1)dy = 0 - 3. 2y(x2 – y + x)dx + (x² – 2y)dy = 0 - -

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Q: An object is dropped from a height of 124 feet. ti = 0, t2 = 2 (a) Use the position equation s = -16...

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Q: Express the general solution of the given differential equation on the interval (0, 0) in terms of B...

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Q: component form or standard basis vectors. Express numbers in exact form.

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Q: Evaluate: A 4e“+C B +C +C D 4 +C (E) None

A: option D integration

Q: Question 4 (sin(3t))^2(cos31)) dt

A: To evaluate the integral ∫sin23tcos3tdt Formula used: Power rule of differentiation ∫xndx=xn+1n+1+c ...

Q: If f(r) is positive then for all 1 <I<2, we have So f(z) dz 7. Select one: O True O False

A: If f(x) is positive then for all 1≤x≤2, we have ∫07f(x) dx≥7

Q: Consider a minimal threshold value for a species to survive, T. One way to add in this factor to the...

A: The answer is shown in below steps.

Q: Solve the problem. Find an upper bound for |E in estimating S (5 - 20) dx with n = 6 steps. M(b-a)* ...

A: Error bound Simpson's Rule :Suppose that f4x≤M for a≤x≤b . If ES is the error involved in using Simp...

Q: 2 -a - 12a? + 70x – 60. Find all local extreme values of f(x) at The FIRST local extreme value, movi...

A: Given :- f(x) =(2x3/3) -12x2+70x-60 find:- All local extreme values of f(x)   

Q: 1. If {an} converges, then {an} converges (C). An+1 Suppose that limn→ 00 1n|= . Then E1 n2"a, conve...

A: We have to determine whether,  1. If {an}  converges, then {an2} converges. True /false? And  2. If ...

Q: 3. Evaluate

A: The given integral is 1/(x-1)2/3 limit from 0 to 3.

Q: Find the extreme values of f (x, y, z) = x + 2y subject to both constraints x + y + z = 1 and y? + z...

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Q: 12x2 Evaluate the integral: -dx 25 (A) Which trig substitution is correct for this integral? Ox = 5 ...

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Q: 00 2 Write out the first few terms of the series 2 (- 1)" What is the series' sum? 3" 57 n= 0

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Q: Find the arc length of the curve r(t) = (2t3/2, cos 2t, sin 2t) from t = 0 to t = 1. %3D

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Q: Let s(t) = 6t – 27t² – 180t be the equation of motion for a particle. Find a function for the veloci...

A: We need to find velocity and acceleration function.

Q: Find the angle 6 between the vectors. u- (1, 1, 1), v- (5, -4, 3), radians

A: Angle between the two vectors can be found by applying dot product of two vectors.

Q: e^x Evaluate A arc sin e^x +c B arc tan e^x+ C arc cot e^x+ C

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Q: 'ind the average rate of change of h(t) = 3 c on t-3 [1,1+ h]

A: Topic:- calculus

Q: Determine the limit of the following 1.3) lim x--> 0 ( 1/x (1/3 - 1 / sqrt x + 9)) 1.4) lim --...

A: limx→01x13-1x+9  

Q: Express the area bounded by the graph of g(x) and thex-axis as an integral on the interval (-00, 00)...

A: We need to express the area bounded by the graph of gx and the x-axis as an integral on the interval...

Q: Evaluate each of the Fo llowings. V bano do V2

A: As per company guidelines we can solve first question. I hope that the given solution will help you....

Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How fa...

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: x? 2. dx x? +9

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Q: the points Pi(6, 3) P2(-3,-5).

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Q: 2- x*y' y + xy' = 1 3D1

A: Given:        -x2y2y'+xy3=1

Q: An inverted conical water tank with a height of 12 ft and a radius of 6 ft is drained through a hole...

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Q: dy Given y = u? - 1 and x = u2 + 1, find dx

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Q: 2. * Given a function whose graph is shown below. The function is continuous on(-0o,-5). O Always Tr...

A: In the graph we can see that graph is continuous at interval (-♾️,-5) because in between (-♾️,-5) th...

Q: An inverted conical water tank with a height of 12 ft and a radius of 6 ft is drained through a hole...

A: The rate of change of the water depth is:-

Q: Let y(x) be the solution to the following initial value problem. dy (In x) y(1) = 1 dx x y? Find y(e...

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Q: Find three positive numbers whose sum is 100 and whose product is a maximum.

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Q: Eind equatons of the following x²-2y²+2²+ yz =20, [4,6-3) W the tangent plane 6 the normal line to t...

A: Solution: f(x)=x2-2y2+z2+yz-20

Q: the following ordinary different is nonlinear? = of them (4) – 2y = 2x – 3y u(4) – x³ y" – 2y' = 2x ...

A: We have to choose the correct option according to the given information

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5, ...

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: Find the divergence of the vector field V(x, y, z) = –5e*"i – e'0xyj + 4e®y=k. (Give an exact answer...

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Q: 00 Determine whether the series E. 2 converges or diverges. If it converges, find its sum. e n= 0

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