(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…

A:

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

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: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

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

A:

Q: Find the derivative dydx of the parametrically defined function x=t+2sinπt, y=3t−cosπt at t=12

A: Given X=t+ 2 sinπt        and   y = 3t- cosπt We have to find dy/dx at t=12 Method used  Chain…

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: Find fxxx for f(x, y) = Sin() at (π, π)

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Q: Show that the function f(x, y) = x² + 2xy is differentiable at any point (zo, yo).

A: Given function fx,y=x2+2xy The sufficient condition for differentiability If a,b be a point of the…

Q: Find the equation of the parabola whose axis is vertical and passes through (-1,0), (5,0) and (1,8).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the equation by Cauchy's integral theorem. 1- dz 2- . 2z(4– z)dz

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

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: Find for the curve dx In (2x) + 5xy + y = 3.

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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: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

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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: b. if x amps of Current prod uces f(s) watts of power in a EeA Circut, find Four ier series for the…

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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…

A: