5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz( ây +2 дхду д д ду?( а

Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…

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Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: Find the distance from y to the plane R3 spanned by uj and u2. (* -3 3 y = -9 Uj = -5 U2 = 1 1

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Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

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Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

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Q: 6. f(t) = , e* sin 2r dr C.. -s(s-1) (s-1)+4 -2 A. s(s+1)+4) В. s((s-1)+4) (s-1)2+4 D. B.

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Q: Find dy/ux of the following 1)lf y = 1/ (1-u) and u = 1/ (1+x)

A: Given y=11-u and u=11+x

Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: dy -1, then -2x If y= csc-(e")+Ve-1. then - Select one: -2 e+1 e2x. -1 e-1 2-1 -1

A: Given, y = csc-1ex + e2x-1  We have to find dydx.

Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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Q: 1. S 3x° + 2x3+7x - 4 dx 2. Sx7 – 48z11 3. S 10t-3 + 12t-9 + 4t³ dt 5z16dz -

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Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: S(x,y,z)= hn xyz +e (30) find f,, and f. 4

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Q: f(y) = 3{/v +Vv- 2V a. f'(V) = 12y O b. 9Ny-6Vy-8/y 12y Oc. 9y +6Vy- 8v 12y O d. 9+6Vy +8Vy 12y

A: Topic:- Derivative  correct option = c

Q: X. 2. dx + cos y ) dy = 0 y A. xy - ysiny + cosy = C B. xy – ysiny - cosy = C C. xy + ysiny + cosy =…

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Q: хе*+2 y = e2x+1

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Q: u-3 15) If y= u+4 and u = 2/x+ 2, find when x = 7 dx %3D

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Q: x3+y²+xy . tet g(x, y) = %3D 6. Find ag(x.y) and ag(x.y) ax ду a2g(x.y) and Find a?g(x.y) дудх дхду…

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Q: f (x,y) =x³ cos y Given df (2, 1) дх of and (2, л). Evaluate ду

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Q: d²y 1. + k?y = 0. dx2 2. at2 3. (x? + у?)dx + 2xydy %3D 0. 4. y' + P(x)у %3 Q (x). 5. y" — Зу' + 2у…

A: Use property of linear and non linear equation

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: According to bartleby guidelines, we are supposed to do only three subparts.  If you want more to be…

Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

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Q: 1. If = 2xy, and y(- 1) = 2, find y(2). dx 3 А. 4e 3 В. — 4е' C. 3 С. 2 2 D. 5 E. - 4

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Q: If f(x) = 1-x* , then an antiderivative F(x) could be Inx| -x А. 6-x C. 5x 3x 5 Inx| – x* 1+x° В. D.…

A: f(x) = 1-x5xAntiderivative F(x) = ∫ 1-x5xdx∫ 1-x5xdx= ∫1x-x4dx= ∫1xdx - ∫x4dx= ln x - x55 +…

Q: 1. (a) Find -and if f (x, y) = 3x? – y² – 5xy y (b) If f(x, y) = 4x?y+ xy² – 7xy then find + ду Je…

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Q: (a) G(r r

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Q: 1 Let F,= (,1]. 00 Then U.Fn %3D n=1 [0,1) .A O (0,1).B O (0,00).co (0,1].D O

A: Option D is correct.