57095-15.7-2E-Question-Digital.docx
Verifying the Divergence Theorem In Exercises 1–6, verify the Divergence Theorem by evaluating
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- (1 point) Evaluate the line integral foF. dr, where F(x, y, z) = -5xi – yi + 3zk and C is given by the vector function r(t) = (sin t, cos t, t), 0arrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. 1. f(x² - y²) dx + 2xydy; C is the boundary of R = {(x,y): 0≤x≤ 1, 2x² ≤ y ≤ 2x) x³y dx + 2xydy; C is the boundary of R = {(x, y): 0 ≤x≤1, x² ≤ y ≤ x} $² 2ydx-3xd y; C is the circle x² + y² = 1 2. 3. 4. ·f (ex² + y²) dx + (e¹² + x³)dy; C is the boundary of the triangle with vertices (0,0), (4,0) and (0,4)arrow_forwardThe plane S can be parameterized by ř(u, v) = (u, v, 3− u – 2v ✔ or ) with (u, v) € D, where D is bounded by u = 0, v = 0, and the linearrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. 3. J. 2ydx-3xdy; Cis the circle x2 + y2 = 1arrow_forward人工知能を使用せず、すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. 4. • (ex² + y²) dx + (ev² + x²)dy; C is the boundary of the triangle with vertices (0,0), (4,0) and (0,4)arrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forwardQuestion 4 of 8 -/ 10 View Policies Current Attempt in Progress Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5 y'dx + 6x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. fsy'dr + 6x'dy = i Attempts: 0 of 3 used Submit Answer Save for Later Using multiple attempts will impact your score. 30% score reduction after attempt 1arrow_forwardTopic: Direction Fields Sketch a direction field for y'=x/y. Sketch your field over the region R={(x,y) | -4x4,-4y4} . Draw direction indicators (arrows!) at each interval coordinate pair.arrow_forward38. Motion along a circle Show that the vector-valued function r(t) = (2i + 2j + k) %3D + cos t V2 j) + sin t V2 j + V3 V3 V3 describes the motion of a particle moving in the circle of radius 1 centered at the point (2, 2, 1) and lying in the plane x + y – 2z = 2.arrow_forwardClairaut's Theorem Let DCR be a disk containing the origin and assume that q : D → R is a function given by g(x, y) = e" (cos y +x sin y). Prove that g(x, y) satisfies the Clairaut Theorem at point (0, 0).arrow_forwardGreen's Second Identity Prove Green's Second Identity for scalar-valued functions u and v defined on a region D: (uv²v – vv²u) dV = || (uvv – vVu) •n dS. (Hint: Reverse the roles of u and v in Green's First Identity.)arrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT Find the integral of the vector function F(t)=(f.,cost)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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