C. Find the following limits: 1) limy-o 2ytan(n/y) sin(n-02) 2) limo2→n Tøl-V

Q: Find the fay and fyy: f(x, y) = xe" - sin(xy) + x³y

A: fx,y=xey-sinxy+x3y

Q: 3. Let h(x, y) x + y sin²x 2¹+ y² 0, if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: 8. Let g(r, 9) = (a) Show that g is harmonic in D- {(7,9) : + (y +3)2 < 4}. (b) How can the funetion…

A: Here given as gx, y=yx2+y2 ......(1)

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: 3. Verify that u(x, y) = x² + 4.x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

A: See the attachment

Q: 1. Let r(t) = (Vt,t + 2t2, e'). Describe the domain of r. 2. Let r(t) = ((t + 2)-1, sin(t), In(1 –…

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Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: 1. Integrate f fe²+³dA where R = {(x, y): x² + y² ≤ 1}. Oa. (e-1) Ob. π(e-1) OC. TE c. Od. Te ле Oe.…

A: ∫∫Rex2+y2 dA where R=x,y: x2+y2≤1

Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: 2y-n у-п lim п cos y y-

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Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Please review the screenshot attached to this request and solve the problem :)

A: Step 1:​(1) f(x,y)=2x2−x4+3y2at(2,3)Using the Power…

Q: Let u(x, y) = x² - y² and v(x, y) = x³ - 3xy². Show that u and v are harmor functions but that their…

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

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Q: Set w(r, y) = cos(xy) where x = t² and y = el-8t, then dw dt Select one: a.…

A: to find the value dw/dt                   dwdt=dwdx.dxdt+dwdy.dydt                     (1)

Q: For F(x, y,z)=(6xsin y+10xz' )i+(3x cos y-4ye"-2y ze" ) j+(-2y'e* +15x²z² )k , find | a function f…

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Q: Let y = f(x) be implicitly defined by xsin y = ycos x. Compute y' in terms of x and y.

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Q: 12. Find a function of f(x,y) such that Vf = 2xyi+ x°j. a. x'y b. xya с. у d. x /y e. x*y f. 2x?y g.…

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Q: Find curl F if F(x,y,z) = 7exy i-8 cosy j +5 sin²z k. curl F = -7xexy k curl F = -7xexy i curl F =…

A: In this question, we want to find the curl of given vector function.

Q: f(x, y, z) = xe*y + y + %3D

A:

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: Let z = g(x, y) = x² + xy³ -y - 6x - 2y +4, where x = r cos (8) and y = r sin(8). дz Use the chain…

A: