Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [(y+e* )dx +(2x + cos y )dy C is the boundary of the region enclosed by the parabolas y = x² and x = y.

Q: 1. Graph the system of inequalities 2х + у S 50 4х + 5y < 160 x 2 0, y 2 0

A:

Q: In Exercises 33-42, determine if the given vector field has a potential. If so, find one. 34.…

A: Solved below

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

A:

Q: A in terms 2A Suppose A E Mn (R)and B. Find the eigenvalues of B %3D of the eigenvalues of A.

A:

Q: 2 у2 | dxdy 1 у 2.

A:

Q: |(sin5 (x)) dx

A: Given ∫sin5x dx

Q: full

A: We will find the double derivative.

Q: 1. Find the solution to the system 4x - Зу +3z %3D 0 2х — Зу + 2z%3 0 бх — 12у + 7z 3D0.

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

Q: Set up, but do NOT evaluate, a triple iterated integral of the function f(x, y, z)=x+ z over the…

A:

Q: The equations for free fall at the surfaces of Saturn and Jupiter (s in meters, t in seconds) are s…

A:

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

A:

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

A:

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: Q3. A market has the following supply and demand functions of a good. Identify the row with the…

A:

Q: 2. Find any excluded values, then solve the following equation: 1 1 I 2+2 IN

A: We have to solve the given equation 1/(x-1)+1/(x+2)=1/2

Q: csc z) Evaluate: lim (x² + e¬®)@¯

A:

Q: Suppose that f(x, y) is differentiable at the point (3, 1) with f(3, 1) = 4, fx (3, 1) = 2, and fy…

A:

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: Question Find fy for f(x, y) = eª ln(y). Sorry, that's incorrect. Try again?

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: Find the slope of the tangent line to the curve 1x² − 2xy + 1y³ = 13 at the point (4,3).

A:

Q: Evaluate the definite integral by interpreting it in terms of areas. 8 (4x - 24)dx stion

A:

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A:

Q: QUESTION 14 Find d²y/dx². x = t + sint, y = t - cost

A:

Q: Determine the exact area between the x-axis and the curve defined parametrically by 2 x(t) = - +² t²…

A:

Q: F. dr. Jc Use Stokes' Theorem to evaluate F(x, y, z) = z²i + 26xj – y°k %3D where C is the circle x?…

A:

Q: Given the Total Cost function, TC = 10 + 5Q?, find the marginal cost function, MC when Q = 10. [2]

A:

Q: Find an equation for the tangent line to the curve parametrized by x = e³t sin(πt) and y = et at the…

A: answer is in next step

Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

A:

Q: L(25 — х?)3/2. |dx

A:

Q: full

A: We will find the polar equation.

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i + 4 sin(t)j; t = 3 r() - () V3 1 T .3 2 2…

A:

Q: Determine the integral of sec^4 (x) tan^2 (x) dx * O 1/7 sec^7 (x) - 1/5 sec^5 (x) + C 1/3 tan^3 (x)…

A:

Q: Suppose that a, b, and c are unknown constants such that f(x) = x² + ax + b and g(x) = e(3z–3) %3D…

A:

Q: АВ C D E F This is a graph of f'(x), the derivative of f(x)

A:

Q: Find an equation for the tangent line to the curve parametrized by a = t¹ — 1 and y = t5 + t at the…

A:

Q: lim (- 3" n→+00

A:

Q: if x 2 a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.)…

A:

Q: Determine a, and as for each arithmetic sequence. See Examples 3 and 4. 29,. 24. -3, -7, -11,... 25.…

A: Since, the student has mentioned to solve only question number 24, so we are solving accordingly…

Q: 13. One group of teenagers bought 8 deluxe burgers, 6 orders of fries, and 6 large soft drinks for…

A:

Q: Suppose f(5) = 9 and f'(5) = - 3. An object moves along the curve y – 3x? f(x) – 5x = 649. For an…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = 2t3 where t is…

A:

Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on…

A:

Q: Find the k component of (curl F) for the following vector field on the plane F=(xe^2y)i + (8ye^x)j

A:

Q: Given k(t)=log_2.4(t+1.6)−3.7 The 3 starting points you would use would be:    . Round answers to 4…

A: Given : K(t) = log2.4(t + 1.6) - 3.7 Basic Function : y = log2.4 t The 3 starting points you would…

Q: ,2 -1 dx 2

A:

Q: The results of an experimental drug trial to treat chronic stultitia are listed below. Women with…

A:

Q: For the quadratic function f (x) = −2(x+1)2 +2, find the vertex, x−intercepts (if possible),…

A: