4. a. Find zx + Zy: given that z(x, y) = tan(x3-3x?y2+2y4) V9-х2-у? b. If u then show that x ди дх ди In(**+y x+y ду 3. I|

Q: If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at…

A: At P1, 2, 3, A→=25ax+195ay+25az. As r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx, at the given point we…

Q: Suppose z = x + 2i and u= 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Substituting z=x+2i and u=3+yi in z+uz-u:  z+uz-u=x+2i+3+yix+2i-3+yi           =x+3+2+yix-3+2-yi

Q: 2. Consider the PDE u; - t ux+tu=0 for - o <x< ∞ and 0 <t< ∞ with u (0, x) = sine x. Determine u (t,…

A:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" +…

A:

Q: A second order Caushy – Euler equation having a solution y(x) = x-cos(4Inx) is O x²y" + 5xy' + 16y =…

A:

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

A:

Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

A:

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

A:

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: y If z = show that = 0. x + y?*

A:

Q: Suppose w = 6xy + In(4 + z²) , x = - , Y 3u + 9v, z = cos(8u). Find dw/dv when u = -5, v = -6. dv…

A: *to find:- Partial derivative of w with respect to v, when u = -5 &amp; v = -6

Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: 2. If z = x° In 2.xy, find at 1,-

A:

Q: 2. Show that 4=x i+y°j+:'k is irotational.

A:

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

A:

Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –…

A:

Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

A:

Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

A:

Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

Q: 2- Verify the following identities : [Sinh( u+ v)+ Sinh(u-vl a) Sinhu.Coshv = Coshu.Cosky =-…

A:

Q: Consider the function. X 10/17 - 12/24 5 Find Duf(7, 1), where u = cos(0)i + sin(0)j. f(x, y) = 8

A:

Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

A:

Q: Assume w = ts³, 4ts) and (x,y) = 6xy of (х.у) - 4х Find as when t = s = 1 %3D

A: Given: From the given expression it is clear that 'f' is a function of 'x' and 'y', and 'x' and 'y'…

Q: a2f Compute Je Je дх' ду f(x, y)= x²y² – sin 2 + xe" and : дхду

A:

Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

A:

Q: If fufe.- fuave diffa Veubable at'xo eI fuave difle Veubable at Xo eI Pi:I R,ists-n prove O…

A:

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: Mixed Partial DerivativesIn Exercises 55–60, verify that

A: (Note: We are entitled to solve only 1 question at a time). Given: w=ln2x+3y To Verify: wxy=wyx…

Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

A:

Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: (a) Prove that dv 1 2 u? + v2 arctan u- + C. 2 u 2, /2/2 ru (b) Prove that I dv du 2 - u? + v2 18 by…

A:

Q: In GL(2, Z,,). det

A:

Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

A:

Q: Suppose w = In(æ² + y² + z²) , Compute dw/du and dw/dv in two different ways: ue3" sin(9v) , y :…

A: GIvenw=ln(x2+y2+z2) where x=ue3vsin(9v) , y=ue3vcos9v and z=ue3vTo find∂w∂u and ∂w∂v

Q: 7) If z(x,y) = x² + y², x=u+v, and y=u-v, find dz du

A:

Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: 2/ Compute fc E.dr and Where F Gxry2=(3+ 12x²,3xy²2 is a line segment from Co,01 to (4,2) %D Fdr =

A:

Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

A:

Q: 18z + 15 Evaluate -dr where 3x2 + 5x + 7 > 0. Зг? + 5л + 7 First substitute u = 18z + 15 dr J 3x² +…

A: The given integral is- I=∫18x+153x2+5x+7dx=∫36x+53x2+5x+7dx Let u=3x2+5x+7 Differentiating w.r.t. x…

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

A: