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Evaluating a Line
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Calculus
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- F. dr. (Check the orientation of the curve before applying the theorem.) Jc Use Green's Theorem to evaluate F(x, y) = (y2 cos(x), x² + 2y sin(x)) C is the triangle from (0, 0) to (1, 3) to (1, 0) to (0, 0)arrow_forwardParametrize the intersection of the surfaces y² − z² = x − 5, y² + z² = 9 using trigonometric functions. - (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the parametrization of the y variable in the form a cos (t).) x(t) = y(t) = z(t) =arrow_forwardFind the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 5 sin²(t)) at t - Ť(7) 6 x(t) = y(t) = z(t) = G 6 Use the unit tangent vector to write the parametric equations of a tangent line to the curve ㅠ at t = 6 = = Submit Questionarrow_forward
- Question function r(t) = (tª In 1, ¹72³, −3e¯³¹). Find the integral /r(t)dt. Consider the curve which is described by the vector b) Find parametric equations for the tangent line to the given curve at the point (0,-1,-3e-³). C Can Can you find parametric equations for the tangent line to the given curve at the point (0, -,-3)?arrow_forwardStokes' Theorem (1.50) Given F = x²yi – yj. Find (a) V x F (b) Ss F- da over a rectangle bounded by the lines x = 0, x = b, y = 0, and y = c. (c) fc ▼ x F. dr around the rectangle of part (b).arrow_forwardLet F(t) = (31³-3, 4et, -sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) = < 0 Question Help: Add Work " Videoarrow_forward
- Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = =(Vx + 4y3, 4x2 + C consists of the arc of the curve y = sin(x) from (0, 0) to (T, 0) and the line segment from (T, 0) to (0, 0)arrow_forwardLaplace theorem of discontinious equation.arrow_forwardConsider the polar curve r=2+ cos O (a) Sketch the curve (b) Set up and then evaluate an integral to find the area that lies inside the curve and above the x-axis.arrow_forward
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