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Let F(x, y) =
(a) Show that
(b) Show that ∫C F · dr is not independent of path. [Hint: Compute ∫
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Chapter 16 Solutions
Multivariable Calculus
- Show that the transformation w = maps the circle x² + y² − 4x = 0 into the straight line 2z + 3 4 Z 4u + 3 = 0. -arrow_forwardIt can be shown that the parametric equations I = x1 + (x2 – r1)t, y = Y1 + (y2 – Y1)t, where 0 < t < 1, describe the line segment that joins the points P1 (x1, Y1) and P2(x2, Y2). Use this fact to find parametric equations with 0arrow_forwardThe parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)arrow_forwardThe parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.) A to B [_____________] B to C [_____________] A to C [_____________]arrow_forwardIt can be shown that the parametric equations x = x1 + (x2 – x1)t, y = y1 + (y2 – yı)t, where 0arrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
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