11. Let F(x, y, z) = = (), and let P represent the path that follows the from (1, 0, 1) to (0, 1,0), and then goes in a straight path F= cos3 sin5 cos7 t line to the point (1,2,3). Find SpF. dr.

Q: Find əw/ar and aw/as when r = n and s = 0 if w = sin(2x – y), x = r + sin s, y = rs.

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Q: Let P= (4.-4). (a) Does P lie on the unit circle? (b) If so, find sin (8), cos (#), and tan (#)…

A: P = 32, -12 = (x, y)   Equation of circle: x2 + y2 = r2

Q: (r,1) = (r sin (f), r– cos (1)), (r.1) = (5,-) s numbers in exact form. Use symbolic notation and…

A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: 2. § F•dï , where F = (ycos(x) – xy sin(x), xy + xcos(x)) and C is the C triangle from (0,0) to…

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Q: Show that ePt cos qt and ePt sin qt are linearly independent.

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Q: Evaluate . 2y2 cos(x) dx + 4ysin(x)dy where C is the line from (0,0) to G,0) and then a line from (,…

A: Line integral over the curve.

Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Use the linearization of f(x) = sin x about an appropriate point Xo to approximate sin 610. Note…

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Q: 2 sin(x) – (-v3) = 0 List all solutions in [0, 27):

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Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

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