(b) If G(x, y) = (x² - y²)i+ 5xyj, find t=sin(u) G.dr along the curve C C:x=t, y=2t²,0 ≤t≤land

Q: - Let f(x, y) =sin(x y − x − 3y+3). (vi) Which of the surfaces below is a graph of this function?

A: Given .This can be rewritten asOn the xy−plane, , if  gives us hyperbolas on the xy−plane.

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: Let sin 3x сos 13лу = sin 3x + cos 13Ty = T(x) of the tangent line at (0, 2), then evaluate T(13).…

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Q: (3/5) What is the directional derivative Duf at the point (3, 1)? Let f (x, y) = x² - y and u =

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Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

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Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x^2 + πχ2 F(x₁ -…

A: Given That: Partial derivative of a function with respect to y is Fy(x,y)=ysin(πxy)+x with the…

Q: 2.(2.3) Let f(x, y) = xy(e² + e³) for (x, y) = R². (1) Find fx and fy. (2) Find an equation of the…

A: (1) fx​=yex+yey+xyexfy​=xex+xey+xyey (2)(3e)x+(3e)y−z=4e  Explanation:

Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

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Q: ) If y = cos2x + 2cosx for 0 < x < 2n. Find the points at which the tangent line is horizontal.

A: Given function is y=cos2x+2cosx for 0≤x≤2π. To find the points at which the tangent line is…

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Find the tangent plane to the equation z = 5y cos(4x - 6y) at the point (6, 4, 20). z =

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Q: Find the length of the curve r(t) = (5 cos(2t), 5 sin(2t), 2t) for − 2 ≤ t ≤ Give your answer to two…

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