Q.No.5 U. = a?u, u(0,t) = 0 = u(L ,t) (B.C) u (x, 0) = f(x)

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

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Q: 2-x2 Evaluate Jenyz dy dx x²+y? 2 Select one: a. Non of them b. 1 /2 C.

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Q: dy If x? + xy – 5y = 5, then at the point (2, 1), dx ||

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Q: (xy+ yz+ xz)dV B = {(x, Y, 2) | 0 < I < 5,0 < y < 4,0 < z< 7} . Do not round. Hint: dV can be…

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Q: 1J, (x) dx I= -J, + J, dx a O dx b O I=J, -2 I=J,+2 dx.c O I= -J, + J dx d O

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Q: Help

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Q: IX. Į F dF where F = (x,y) and C is the straight line from (2,3) to (4,0)

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Q: Determine the location of all extremes and show what type the extremes

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Q: Evaluate Əw at (u,v) = (1,2) for the function w(x,y)=xy-y²; x = u-v, y = uv. ди OA. -1 B. 3 O C. 1…

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Q: Find u x v, v x u, and v X V. u=i-j, v=j-k

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Q: Find df and dxo f , and write (dxo f )(X – Xo). (a) f(x, y) = x³ + 4xy² + 2xy sin x, Xo = (0, –2)…

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Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: du - = In ( – u) +C If u<0, then u A True B False Question 2 8x – 16dx=2 x– 2 dx A True B) False

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Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: x¹ + x² + 1 I(x² + 1)² -dx.

A: The given integral is: ∫x4+x2+1xx2+12dx Evaluate the given integral.

Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

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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: 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: dy If y = e7z+16 then- dx O 112e7z+16 O 8e7z+16 O 6e7z+16 O 7e7z+16 O 16e7z+16

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Q: Finel the Laplace Trans Form 21 Ans. F(s)= 2(1-e ") 11)

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Q: Ut +Uxx =0 , Uxl0,t) =0, t7. Ux (1,f) = 0, t70 O<a<M, tro. UC2, 0)

A: The heat equation with Neumann boundary conditions is as follows. ut=c2uxx, 0&lt;x&lt;L,…

Q: dz The value of o (1+ z where C is the ?) i =1 is 2 contour z |

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Q: Find R f(x, y) dA where f(x, y) = x and R = IR F(x, y) dA = [3, 9] x [4, 6].

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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: xxx, xy(Rxy →→~Ryx) - vx~Rxx

A: To prove ∃x Rxx , ∀x∀yRxy→~Ryx ⊦∀x ~Rxx

Q: Find the distance d(u, v) between u and v. 1 3 [+0] 3, V = 1 2 d(u, v) = U =

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.