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Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

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: Let y = 2x + 3x + 2. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay 2 Submit…

A: We have to find change in y

Q: 1. Using the first prine =) , show that (1 – x*) + 4nxy = 0. %3D 2. If y = 1+x2, + qx2+rx +s passes…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3)- find ahe pr patikular solustien of theditfrential equatisnx+Cx =CL given the x6)=a Ax 20 at t=o…

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Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

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Q: Verify the given linear approximation at a=0 . Thendetermine the values of  x for which the linear…

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: 1.20 * Prove that the flight-path angle is equal to 45° when v = 90° on all parabolic trajectories.

A: Solution

Q: Let flt.v) = y+3r²e!. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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Q: Again differentiate with sespect do 'x get we A cost- B Sinz A cosz + BSiny) { from @ d +

A: Please refer the attached image for complete solution.

Q: we Gtokes theos em. to pvaluate Fel8 whes F=Z?E t y?; +XK and cf1,0,0) (0,1,0) andlogo, i) nr…

A: By using the stokes theorem we have to evaluate ∫CF·dr where F=z2i+y2j+xk and C:1,0,0,0,1,0, and…

Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: 3.2 Evaluate (1² + y³)dz where z = r+ iy with y the path on line from z = 2+i to z = 1+ 2i.

A: Topic:- complex number

Q: D.4) show that is boundled) abng the if I sinz line&CXoy):dX-By =of Straight then

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Q: = Let y 2x2 linear approximation + 7x + 4. If Ax = 0.1 at x = to estimate Ay 2, use

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: 2 Evaluate (2² + y²)dz| where z=x + iy with y the path on line from z=2+i to z=1+2i.

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Q: 16. Let y = 4x² + 7x + 4. If Ax = 0.2 at x = 2, use linear approximation to estimate 4y Ay 2

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Q: +3 fn d the deivotive of this funckio slape of the tonpent On d the line ot (4,1).

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Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: 3.2 Evaluate (2² + y² )dz where z = x + iy with y the path on line from z = 2 +i to z =1+ 2i.

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Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

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Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: Q4: Let z = 2x² – y2 . Find all points at which |Vz| = 4. Then find V|Vz| at the point (1,4).

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Q: 11, If PQ = OR, JK = 3x + 23 and LM = 9x- 19, find PK. %3D %3D %3D K J R. %S'

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Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

A: We have to find grad(divV ) at (2,-1,0) where  V = (3x2y-z,xz3+y4,-2x3z2)

Q: A bug is crawling through the ry-plane in such a way that its coordinates (r(t), y(t)) at time t are…

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Q: 3. Given the two following left rights: x = 3 +t D: y = -2 + 2t, where t eR z = -1+ 5t D2: (x,y,z) =…

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Q: Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

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Q: e-", if 0 3,

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Q: What is v(t,) at t, in the given equation of s below? Also, what is v(t,) if t = 3? s = vt +1 1 1 ;…

A: Given s=t+1

Q: 8) Confirm that the stated formula is the linear approximation at x =0 %3D (1+x) =1+15x

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Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: 3 3 O Find the rot of fX)= x * - ? pplying Secnt Method and Regula Falsi Methock twice with initials…

A: Given that,f(x)=x32-32The root of the above function is calculated using Secant methodand Regula…

Q: 1) If Euler's method is used to approximate y(t), the local truncation error, T;+1 is defined as…

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

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Q: 4. and A= Find flA) where f lt) = t"-2t+3t+ 3t +2 て %3D %3D て

A: Given,  A=124-1 f(t)=t4-2t3+3t2+3t+2 Find: f(A)

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

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Q: Let f(x, y) = 4x + 3y and let 7 (t) be the line segment from (1, 1) to (–2, 5). Then 7 (t) =…

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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: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?