oA Vg iai cjá r = |i| g(r) = s7 = xi + yj + zk S

Q: 2. f(t) = e4"(t² + 3t + 5)u(t) %3D

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Q: f (x, y) = 3x2 + y + 4xy + 8 %3D af(z,y) when x = 2 and y = 1? dy What is the value of %3D

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Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

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: Q/ Let X be the r.v such that E (X) = 2 , E(X²) = 2a , E((2+aX)²) = 2a³ Find the value of a

A: We have given that, Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²) = 2a3 We want to…

Q: z dz In order to evaluate JA2 – 9 we use the substitution sec e I= 3 sec 0 9. I= -sec 0 4. I= sec 0

A: Indefinite integral by substitution method

Q: H In OJ, GH = 9, KL = 4x + 1. Find x. R 5. 5 S. GK

A: Given: GH=9,KL=4x+1  If from a centre a perpendicular is drawn to the chord, then a chord is divided…

Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: D = {(x, y) E R² :0<x <∞, 0 < y<∞} olmak üzere, [ rye--v°dA D.

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: Q3: if it was A(x, y, z) = x?yi + y?zj + z?xk and Ø(x,y,z) = xy + yz + zx find (a) A. (VØ) (b) Ø…

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Q: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

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Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

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Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: 9. T: R² → R², T(x, y) = (x + 2y, y – x) 10 T. D2

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Q: df f(z, y) = x² + y°; T = ť° + t°;y= t³ + t, att = -1 %3D equals Select one: O a. -1 O b. 144 Oc. 64…

A: f(X,y) = x2+ y3 Find df/dt at t = -1

Q: ize P= 3z + 4y E to 21 + vS 16 27+ 3y S 24 z20, v 20

A: Introduction: Linear programming is the most basic method for optimizing a problem. We can use this…

Q: Q3: If z = f(u,v,t) = Z 3u? + v2 ,u = tet , v= te-2t Then dz at (2,2,0) at

A: Topic:- partial derivatives

Q: e where r is jiven peu'ametor! Fnd f'6).

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Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: There does not exist r E Q ə r² = 2 ylgn ihi

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Q: F.ds, W by the pl

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Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²)= 2a3 Find the value of a .

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Q: C is given by x = 4t and y = 3t, where t runs from 0 to 2. Evaluate (y/x)ds 45/2

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Q: Differentiate. V(t) = (t + 7e')/t %3D 3 7/)eIn(e) + v7 * V'(t) = 2

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Q: Find partial derivative.

A: We use product rule to find the partial differentiation.

Q: Find projy u. v = 7i- 3j + k, u = - 4j + 3k 105 O A. 45 15 59 '- 59 + 59k 60 45 O B. - 59i* 59k 12…

A: Given vectors are,  v=7i-3j+k and u=-4j+3k The objective is to find projvu Now, u·v=-4j+3k·7i-3j+k…

Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: jx-P,(x)dx, n= 0,1,2,... -1 Q.3 Evaluate:

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Q: Q2: * Q2: y" + ay' + by = f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t? – 1 %3!

A: Giventhat:¯y+ay'+by=ftand yp1=et+t2-1 and yp2=e2t+t2-1To find:¯a,b and ft

Q: ii. (x + y)dA Where R = {(z, y)|1 < x² + y? < 4, x < 0}

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Q: f(2ecz tan z - 6z")dz=_ • tan z+z+e secz+z+e • secz-z+e - secz-z+c •- secz+z+e

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 10 dz where C2 is the top half C2 that is C2: |2| = 2 with z = re", 0 < %3D

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Q: Lặi T(z) = -6zª +2² – 1 and U(z) = 2 – 4z + 3 Find T(2) + U(z). %3D OA -6z + 22+-4z +2 OB -72 +2 OD.…

A: Tx=-6x4+x2-1  &amp;  Ux=2x3-4x+3

Q: Dketch a 3-dhensranal grapn of the equetey 1巻)Z-6-2ーy2 ×Z0 42O 2) 0-

A: 1) given equation to draw the graph is z=16-x2-y2 ,x≥0,y≥0 since x,y are positive the graph will be…

Q: I Y=t5メPYove th y-2(21くるど

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Q: Q5/ If w = f(x,y),x = rcos0,y = rsin0 show that: af af 5² + 1 dw Əw. -)² + ar r2 a0 дө

A: The chain rule can be used to calculate the derivative of the complex functions. The function which…

Q: cose r cose r dz dr de r2 T/2 T/64 TU4 T/16

A: As per our guidelines, I can answer maximum one question and three subparts of a question. So here…

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: The x, y, zER, subject to the condition yz + zr + xy = 12. Then greatest value of ryg is (a) 6 %3D…

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Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: a. The y' for y = (u – 4)z and u = x² + 4 b. The y' y = Vu and u = Vx

A: Given;          a.  y=u-432 and u=x2+4b.  y=u        and u=x a. Solve for y'…

Q: Solve Utt - c?uxx = 0, –n 0, %3D u(x, 0) = f(x), u(-n, t) = 0 = u(n, t), ux(-n, t) = 0 = ux(n, t).

A: Given: The PDE is utt-c2uxx=0 , -π&lt;x&lt;π,t&gt;0.

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: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+aX)²)= 2a³ Find the value of a.

A: E(X)=2E(X2)=2aE((2+aX)2)=2a3

Q: Find r(t) if r'(t) = ti+ efj + 2to2t k and r(0) = i+j+ k. r(t) Need Help? Read It

A: Given data is: r't=t2 i+et j+2te2t k r(0)=i+j+k To find the value of rt

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Q2: y" + ay' + by f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t2 – 1

A: