00 \:YE2 53504059321845...Chapter FourPartial derivativeAdvanced CalculusDr. Khalid UtubSheet 7azQ1:- Find theazandaxif Z = x* sin x y³.дуQ2:- Find fp , fe , fo if ƒ(p,0,Ð) = p² cos ¤ sin 0.2уQ3:- Find fx , fy if f(x,y) =y+cos x'dwQ4:- Expressin term of t , if w =+x = cos? t , y = sin² t and z = ÷.dtdwin term of t, if w = xy , x = cos t and y = sin t, when t =Q5:-FinddtawQ6:-Findawandarifas1) W = x²2) Wx = r -s and y = r +s+ yLn(x² + y2 + 2z) , x = r +s, y=r – s and z = 2rs.eya2wa2wQ7:- If W = xy +y2+1'Show that%DдхдудудхQ8:- Find the second order partial derivatives of the following function1) f (x, y) = x²y + cos y + y sin x3) r (х, у) 3D Ln(4х — 5у)= Ln(x + y)x-y2) r(x,y)4) f(x, y)x+yawQ9:- Findi = 1, ... ,n if W = cos(x1 + 2x2 + 3x3 + …+ nxn).axi1awQ10:- Find,i = 1, ...,n if W = ( E1xi)ñ.a²z, (c >0, constant).azQ11:- Show that the following functions satisfies the heat equationatc².əx²1) Z = e-t sin-2) Z = e-t cos-a2za2zQ12:- Show that the following functions satisfy the Laplace's equation+= 0.Əx2ду?1) Z = Ln(x² + y²) + 2 tan-122) Z = x2 – y² + 2xy 3) Z = e* sin y + e cos xR1R2a?R a2R4R2Q13:- If R =. Show thatR1+R2ƏR ər?(R1+R2)**awQ14:- Let W =f(u), where u = x + 2y + 3z. Show thatawaw= 6azdwдуduQ15:-Given that w = f(u,v), u = x + y and v = x – y. Show thata²w2)дудхa2fa2faw aw1)дх дуa2w a2w3)дх2 ду?a²f+ди?= 2ди?dv²a²wa2wQ16:-Show that (x² + y² + z²) z satisfy three-dimensional Lap lace's equationəx2a2w= 0.əz2ду?ду1Q17:- In polar coordinates prove thatarII

Answered: Image /qna-images/answer/bcd43f6b-598e-4e20-9f71-831e42b9315e.jpg

Answered: az Q1:- Find the az and ax if Z = x*…

az Q1:- Find the az and ax if Z = x* sin x y³. ду

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

Similar questions

Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial derivative fx, fy, and fz of (x + yw )2 – ez – 2 = 0 and f ( x , y, z ) = 2xyz + tan x + y sin z Make the solution detailed and clear IN A PAPER.
calculate....along the curve curve in the first octant given by x^2 + y^2 + z2 = 4, (x − 1)2 + y^2 = 1.
1. Show that f(t) is continuous at t=0 2. Use L'Hopital's rule to find the 1st and 2nd derivatives of f(t), evaluated at t =0
prove if u(x,t)=1/2(sin(x-t)-Sin (x+t) ) is Solution to partial derivative wave equation 2 u/partial derivative t2 = partial derivative2 u / partial derivative x2
Show that bothy= sinx and y = cos x satisfy y" = -y
Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are differential function of (x) , with two examples?
First and second derrivative of: Cos(xy)+secy=5
Limit _π/2 toπ/2 integral (1+cosx) dx
Prove cosh 2 x - sinh 2 x =1
Suppose ƒ is differentiable on (- ∞, ∞), ƒ(1) = 2, and ƒ'(1) = 3.Find the linear approximation to ƒ at x = 1 and use it to approximate ƒ(1.1).
Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every where.
prove the identities assuming that the appropriate partial derivatives exist and are continuous. div(F + G) = div(F) + div(G)