Let x' = K, then w(x,.x2) = e?r -1 3 5 2 Select one: O True O False

Q: sn'x プェ Sec'x-1 from [o, of 2.

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Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th

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Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: ue of the det e 16 is

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Q: 2. If z = x° In 2.xy, find at 1,-

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

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: az Find for z = x'y'eV

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Q: -s Jatx? 3. 4-/ sinx coss dx |

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: Sm Vx dx

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

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

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Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

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Q: In Exercises 5–12, find and sketch the domain for each function

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Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: (z In z + 5)dz

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: 3. If x = (sin t+cos t), y = (cos t-sin t), (1 < t < 4), evaluate ip, dt. dt dt

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: Show for Re(z) > 1 -dx = r(z) (2). et - 1

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Q: dy sin(x + y) dx

A: Given , dydx=sin(x+y) Substituting u=x + y dudx=1+dydx Substituting dydx=sin(x+y) in dudx=1+dydx…

Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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Q: Put that: coshx- hel x+Jx=I/,.- cosh x= lml x+J xI/ メン」

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Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: Assume that y= 5x and de/dt = 2. Find dy/dt. Select one: 10 O 5 O 2 1

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: If s = 3/t + 1, then ds Preview %3D dt

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Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: for w = x sin y +y sin x + xy. W yx Q2) A) Verify that wry

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Q: d'y on of x

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