Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D dx2

Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other…

Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

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Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: Q3:- Find fx, fy if f(x, y) = y+cosx 2y %3D dw

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Q: dz Find when u= 0, v= 1 if z= sin(xy) + ysin(x), x = uv, y3Du² +v?. du

A: Given  z = sin(xy) +ysin(x)              x = uv and y = u2 + v2  Substituting x and y in z we have…

Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Fain the par hicul ar foluhion 4 DE . 9xy dy ; uh en x= 2,y=1 4xy° dy = 2y (1+ y?) dx ; when x- 2…

A: In this question we will use basic of calculus i.e contact of solution of differential equation. We…

Q: If z= t(x,y), where X = rCOse and y= rsine, %3D Show that 12 dz 12 dz dz dr dz del + dx

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Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? %3D Select the correct response:

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Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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Q: Be w = (u2 + v2)3/2, where u = e-t sin(θ), v = e-t cos(θ), calculate: ∂w/∂t and ∂w/∂θ

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Q: - choose the correct answer If y = t^2/(t^2+1) and t= v(2x+1) the = dyldx %3D 1/N(2x+1) O 2(x+1)^2 O…

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Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w v2 fuu + u² fov – 2uv fuv - ufu - vf dx2

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Q: show that if y=cosx/x, then d^y/dx^2+2dy/xdx+y=0

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Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

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Q: a2f Compute Je Je дх' ду f(x, y)= x²y² – sin 2 + xe" and : дхду

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Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: * Q9 If y = cos(x + y)dx + (3y² + 2y + cos(x + y)) dy = 0, then M = cos(x + y), N = 3y² + 2y Ttue…

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Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: Q:Ifx= sin 6, y = 0,y = cos pe, prove that (1-x )y,-xy,+p°y = 0, %3D dy where y, dy and y1 d

A: Here given that x=sinθ, y=cospθ Taking derivative of both x &amp; y with respect to θ, we get…

Q: 2- FIND f (t) or fis) AS APPRO PRIATE A) L}Je costdt COS ) y+2メ=8(t-)0)00)=イ

A: Here we use basic definition of Laplace transform

Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

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Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

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Q: dw If w = x2y sinz - 3zey, find dz 6. O a. dw =x?y cosz - 3exy dz O b. dw =2x2y cosz- exy dz O c. dw…

A: Find the partial derivative of w  with respect to z

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² fuu + u?fov – 2uv fuv – ufu – vfp dx2

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: If x"y" = (x + y)"** m. m+n Then, P rove that dx?

A: Double derivative

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Q: 1. Differentiate F(t)= e4t° sin sin 2t [Hint: y = e", u = 4t³ sin 2t.]

A: In this question we have to solve the differentiation of the function.

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…

Q: Find Vf(x, y) if f(x,y) = e** cos y ..... ...

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Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.