z# sin(z²yz) Let f(r,y, z) = %3D 12 find at the point (3,0,0) O 4 O 12 0 6 0 8

Q: -32 %3D Find the gradient Vf (x, y,z) OF f (x,y.z) = e sin 3X cos 3y

A: The given function,      fx,y,z=e-3z sin 3x cos 3y

Q: Ind. Dep. Type Order Linear Degred Var. No DE. Var. o DE yes I 1 yxy x* Uxx + 5u uy = 5x?uyy 3.…

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Q: Slowing initial value problem using Laplace transforms: y"- 6y + 15y 2 sin(3t), y(0) = -1, y/(0) = 4…

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Q: (a) f"(x) = e* – 2sin(x), f(0) = 3, f(T/2) = 0 (b) f"(t) = Vt – cos(t), f(0) = 2, f(1) = 2 -

A: The formula used: (i)∫ex dx=ex+c(ii)∫xn dx=xn+1n+1+c(iii)∫sin x dx=-cos x+c(iv)∫cos x dx=sin x+c

Q: use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02) given g (x, y, z)…

A: We have to use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02).

Q: x' = y, x(0) = 1 y' = - x, y(0) = 0 at t=1.

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Q: z = cos(x² + y²), nd Əz/əu and Əz/av. The variables are restricted to domains on which the functions…

A: The given expressions are z=cosx2+y2,  x=ucosv, y=usinv. Find ∂z∂u and ∂z∂v. Let f  is a function…

Q: Curves Pind the Integral of I y=22 y = 8x2 ||= xy 19 = xy | Let te Isff(ay)dA= [f, fuw) ]J(uw] dA If…

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Q: √ [F(x₁) Evaluate f(x, y) ds. f(x, y) = xy S: r(u, v) = 8 cos ui + 8 sin u j + vk Osus, OsvS1

A: Given that   we have to evaluate ∫S∫ f(x,y)dS  and                                fx,y =xyS: ru,v =…

Q: f(x, y) = sin(xy) + x^2 ln(y) Find fyx at (0, π⁄2)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Mediante la regla de la cadena encuentre dz/ðs y dz/ð. 7. z= xy°, x= s cos t, y = s sen t 8. z =…

A: According to our company;s guidelines, I can only answer first three subparts of the question, since…

Q: dx dy Assume x and y are functions of t. Evaluate dt = - 92, with the conditions = - 8, x=4, y= - 2.…

A: For first expression, The equation is 4xy-7x+4y3=-92. The value of dxdt=-8,x=4,y=-2. For second…

Q: f(x, y, z) = tanxy xy;f,(1, 2, -2) %3D

A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Q: xy' + y = 0, y(4) = 6 y'cosh?x = sin² y, y(0) = }7 TT y' = -4.x/y, y(2) = 3 xy' = y + 3x* cos²…

A: As per guidelines, I can answer only one question. Since you have asked for multiple questions, so I…

Q: (a) y" + (sin x)y' + exp(x)y = 0 around r = 0 1 1 4 +... 1 1 Ans. y(x) = ao 1- 2 + a1 ,x ER +... 6.…

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Q: Ax-0 AX Ax-0 HW. Find if y = Vx and x > 0 dx Somo Rulos of Dorivotiv

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Q: xydx - (x^2+3y^2)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)dx + N(x,y)dy…

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Q: dy dx Assume x and y are functions of t. Evaluate for 4xy - 2x + 4y³ = - 28, with the conditions dt…

A: Given,            4xy - 2x + 4y3 = -28 and dxdt= -16, x = 4, y = -1

Q: (a) f"(x) = e* – 2sin(x), f(0) = 3, f(1/2) = 0 (b) f"(t) = Vt – cos(t), f(0) = 2, f(1) = 2 -

A: The formula used: (i)∫ex dx=ex+c(ii)∫xn dx=xn+1n+1+c(iii)∫sin x dx=-cos x+c(iv)∫cos x dx=sin x+c

Q: S[[ 2xdV where E = {x, y, z) |0 < y < 2,0 sxs4-y²,0<= <y} E [[[ vz cos(x* kiV where E = {x, y, z)…

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Q: Hyberbolic (D5 – 2D³ – 2D² – 3D – 2)Y = 0 ANS.y = e¬*(c, + c2x) + Cze2* + C4 cos x + C5 sin x

A: Given: D5-2D3-2D2-3D-2Y=0 So, the auxiliary equation is: m5-2m3-2m2-3m-2=0 Now solve;…

Q: f(z) = Cosz %3D ,0< Izl f(2) = sinz 3D 0< zl %3D f(z) = e-V, 0< Izl %3D

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: A. Find the linearization L(x.y.z) of the function f(x.y.z) = V2 cos2x sin(y + = (0.0. ). Then, find…

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Q: (6) The total differential of the function tan-1(x/y), where (x, y) (0,0) is ydx – xdy (a) x2 – y?…

A: Given that f(x,y)=tan-1xyTo find the total differential equation of f(x,y)=tan-1xyThe total…

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: xz -1 cos (xy-x*) If w = y(x- mz)i + yz² j +In k and f=w · *+m)" W y find at point (0,2,-m): (i) the…

A: Given - If w = yx - mzi + yz2j + lnxz - 1x2 + mk and f = w ·cos-1xy - x2yj To find - Find at point (…

Q: r=√{(e^{-y}xcos(x)-e^{-y}ysin(x))^2+(e^{-y}xsin(x)+e^{-y}ycos(x))^2} find r.

A: Given information: r=e-yxcosx-e-yysinx2+e-yxsinx+e-yycosx2   Formula used:…

Q: y(2x^2-xy+y^2)dx - x^2(2x-y)dy = 0 when x=1 ; y=1/2 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y)…

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Q: Ã(x, y.z)=(4xy²-x')i+(2e"-ycos2xj+(x'siny k . and Əyəx Əx' əy² 'Əxôy Find:

A: Given -  A→(x,y,z) = (4xy2-x5)i^ + (2exy-ycos2x)j^ + (x3siny)k^We have to find the following -…

Q: 1. F = cos y i+ xyj + yk, A. i+j+(y-siny)k B. i+ (siny-y)k C. j-(2y-siny)k D. 3i5j + (sin y)k E.…

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Q: i) LSCOS(siny) dx dy = 15 -15 a.- 14 b. d. 14 29 -29 14 c. 14 ii) area bounded by x = 1, y = 1, x =…

A: As per our guidelines, answer first three question of a multiple question. So please resubmit the…

Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: x²e*= sin(x² yz) Let f(x, y, z) %3D 12 o f find dydzd' x at the point (2, 0, 0)

A: Expanding the terms as power series then differentiating

Q: Gram - Schmıdt. or thogonalizan -wej) on Let P, = sın «x a<x<b P = Cos a x. a sx 4. b SIn adx a…

A: Gram Schmidt ortho normalization process:- For vectors v1, v2, ......, vk the ortho normalized…

Q: f(x, y, z) = 6x y 25 V f(x, y, z) = %3D 5 f(x, y) = cos (6x) + sin (3y) = COS Vf(x, y) = %3D

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Q: Using Rationalizing Substitution S- O In(y) + C O Arctan(y) + C O2Arctan(y) + C O2ln(y) + C dx…

A: ∫dxxx-1Substitute y=x-1→dydx=12x-1→dx=2x-1dy=2∫1y2+1dy

Q: (g) f (x,y,z) = x² + y? – 2z? + zlnx in P(1,1,1) (h) f(x,y, z) = e*+Ycosz + (y + 1) sin -1x in…

A: Gradient is a vector quantity that represents the rate by which function value is changing. Gradient…

Q: ORTHOGONALITY OF BESSEL FUNCTIONS J x J, (ax) J, (ßx) dx = 0 %3D where a and B are the roots of Jn…

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Q: dy + y csc x = sin x is dx The integrating factor of the linear DE of order one A cot?x B csc x cot…

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Q: (x-2y) dx + (2x+y)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

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Q: dx dt Please give an exact answer. If z² = x³ + y², = dt 1, dy dt Provide your answer below: = -1,…

A: The objective of the question is evaluate the derivative of the given function at given point.…

Q: II. Test for exactness. If it exact, solve. 1. (x- 2y)dx – (2x + 5y)dy = 0 2. (4x³y-18x² + y)dx+ (x*…

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Q: Integrate f(x, y)= y cos xy over the rectangular O ≤ x ≤ π, 0 ≤ y ≤ 1

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Q: y' = x+y+xy, y(0) = 1 at the point x = 0.1 (h=0.02) Use 4th order RK

A: Given y'=x+y+xy where y=1 when x=0. The objective is to find y0.1 using Runge-Kutta 4th order…

Q: z = uv + v2, u = tan- x, v= y(x² + 1) Find zxy

A: We have to solve

Q: dx Assume x and y are functions of t. Evaluate for 2xy - 7x + 2y = - 20, with the conditions = - 6,…

A: topic- derivatives

Q: дz a) yz = ln(x+z) ах 2²u b) u = √√r² + s², r = y + xcost, s = x + y sin t дху c) z = 4ex Iny, x =…

A: Partial differentiation.