If vy 3x P(x, y) is true, then 3x Vy P(x, y) is also true O Yes O No

Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: If f(x,y)= Iny, then Vf(x,y)= :- Select one: O True False

A: We know that, gradient is a vector function. ∇fx,y=fxi^+fyj^

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: Express dw and ds interms of rand s, where w = x2 + y?x = r – and y = r +.s = 5rand w as = 38 4rsand…

A: topic - derivatives note : As per bartleby guidelines, we are supposed to answer only first question…

Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

A:

Q: Let W(x) = W[y,, y2, Y3] , where 11 V1, Y2, Y3} are solutions to y"+3x y' -4y 0. Then W" =3 W.…

A:

Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

A:

Q: If w= Xze' y=va²–x² , z=Sirx, then ( dw is

A: we will derivative by using chain rule

Q: et z = r²y – ry², I = e *,y= e*, then which of the following is O a. 2et + 2e 2t O b. 0 OG -2e4 – 2e…

A:

Q: 1 Evaluate dz, where (i) C is z+ = 2 .2 +1 C

A:

Q: What is the general solution of (r* + s) dr + s² (3r + ks ) ds = 0 where k is a constat || O 4rs + r…

A:

Q: Calculate fryr if Ar.y,z) = &r-9*y³-z³. OA foe =-322 OB fye =0 OC None of these OD fye = 3r2-3y2-322…

A: We have to find the partial differentiation of the function with respect to X y and z

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

A:

Q: x then ux is XX If u = V y %3D

A:

Q: If f(x, y) = 7xey + 7y Inx, then is given by: дудх O 49e5y + 7/x 35eby + 7/x O 25e5y + 7/x O 35e5y +…

A:

Q: Which of the following is true if* f(x, y) = 2- 2xy + xy³ + 3y? frz (x, y) = 6x fyy (z, y) = 6+ 6xy…

A: Given that f(x,y)= x^3-2xy+xy^3+3y^2 then find the fxx, fyy, fxy.

Q: ces. 1 W= d b such that Z = ax + bY. calars a and b such that w = ax + bY? = 0, is it true that a =…

A: We have to find the following conditions according to the given information

Q: Q111f и %3D (1 —2ху + у?)""/2, Prove that: ди ди y əx y? u3 У ду

A:

Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

A: This question can be solved using the concept of derivatives.

Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: Q3: van fy = xy*-1 + x",In(x) f(x,y) = x +y* • if it was True false

A:

Q: VXEN, 3yEZ s.t. x + y^2 = x - y O TRUE O FALSE

A:

Q: /| (9x + y – 2z) dS. Is Evaluate S: z = x + 0 < x< 4, 0 <y< 7

A: Given: ∫∫S9x+y-2zdSS:z=x+y2, 0≤x≤4, 0≤y≤7

Q: B = {(x,y xs2, -a sy s3, 0£21} SS, x*yz²dV 2 'B

A:

Q: 2. (Z, * ) where * is define by a * b = a - b.

A:

Q: 3 If U<xy+ yZ +Z X Find d Ce, y,2) y it bcist. V =X +Y+Z, W=)X YZ %3D

A: Given : u= xy + yz +zx , v= x+y+z , w = xyz To find: ∂(x,y,z)∂(u,v,w) Solution: Let   A = u- xy - yz…

Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: What conclusions can yo WD DY because ZX is WX = XY because of The Find the value of x to the ne 8.…

A: Using Pythagorean therom.

Q: ở =, then If f(x, y, z) = In(2 + x² – 2y² – 3z), Duf(2, –1, 1) = A) % 11 V3 В) 11 C) D) - E) OC O D…

A: The solution is given as

Q: If W= Wly,, Y2, Y3] where y1, y2 , y3 are twice diffferentiable, W" = W. Select one: O True O False

A:

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: If u = is X then uor y OA. 33 OB. - 4 Vyx y a - 8 Vy x3 OD. 4 Vy x3

A:

Q: noger whare : y's Fl7. ) Homogencus writter us Example 2: y'- 3yay %3D

A:

Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: Given: if fx,y,z=x2y2z2 then fxyzx,y,z=2xyzx2y2z2 We have to state if the given statement is true or…

Q: 3) yv1+x²dx + x/1+y?dy = 0 (1+v1+x²)(1+/1+y²) Ans: V1+ x² +/1+ y² In +c (Bali, 2007) xy

A:

Q: If f (æ, y, 2) = x²y – 3yz + 2æz* , then f (2, 1, –1) is 2 O 5

A: If f(x,y,z) =x2y-3yz+2xz3, then f(2,1,-1) is

Q: Disprove the statement by giving counterexamples If m,n ∈ R, then |m + n| = |m| + |n|.

A: The equation is m+n=m+n.

Q: If C is given by x = 2t, y = −2t, z = t, 0 ≤ t ≤ 2, evaluate Z C (x − y + z) ds

A:

Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: Azy'dz dy- 2y (y- 1)dy select one: O True O False

A:

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

A:

Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: Be w =x + 2y + 2°, x = , y = r + In s and z = 2r. Determine and when s = 1 and r = 2 ds Or

A:

Q: SA (xit) = S'y St ot) SHL %3D Subject to Con d'tions Detesmine the expre ssion tor u(xst).

A: Given partial differential equation is                                 ∂∂tux, t=∂2∂x2ux, t…

Q: If x = t² and y = t³, then y O t O o O 3/4t O 3/t O Other: =?

A: In this question, we have given the values of x and y in the form of the variable t and we want to…