Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

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Q: (c(2z+y), %3D ue of c in the joi F of W.

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Q: Let y = 2x + 2x +3. If Ar = 0.2 at a = 2, use linear approximation to estimate Ay %3D Ay Submit…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

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Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: 2z+1 37 Prove the equation through integral calculatipns. dz < 5+z? 2

A: We will do the proof step by step.

Q: 4. Show that evx dx = 2Vxevx - 2ev + C Hint: Make a substitution first before doing integration by…

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Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: nto v. t of u orthogonal to v.

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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: It G acts set tdansikivey then show that y Salgdnap Hof 0n A by to the actioh af en A fusthus then…

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Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: Find the guneral antiderivative of the funchion. (check your answar answer by differentiation.) 14)…

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Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: 1 Find the local linear approximation of f(x) = , at 3+ 1 Tg = 2, where Az = I- 2. NOTE: Enter the…

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Q: F/ prove JhaT cosh(z1+2=)=Coshz.coshaa + Sinh2,Snhze

A: Note: You have not mentioned which question to be solved. Here we are providing answer for 1…

Q: au Show that the local truncation error at the pint (ih,jh) of the Crank-Nikolson approximation to…

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Q: 4. Using the definition of sech x ,x 0 in terms of e , prove that 1+V1-x2 sech x = In ,0<x <1 Hence,…

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Q: Nove the followingTuation sutisfied Cauchy - Rieman. s oes W = Z 4 equation

A: For a function of form w=f(z)=u+iv is said to satisfy Cauchy-Riemann Equation if ux=vy  and uy=-vx…

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: Q2 A) for F= 2xi-3Y3+K %3D prove That div( curl È)=0

A: Given :          F→ = 2x i - 3y j + k   To prove that div(curl F→ ) = 0

Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Find g: R R, continuous in [0. ) and position in (0, ) satisfying g1) %3D )dt

A: Here we have,  g:R→R, continuous in [0,∞) and position in (0,∞) Also given g(1)=1 and…

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" - Зу" + Зу'…

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Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: Find the lineanzation LlXiy) of f (iy) =x*-5Xy at (2,1). Then use the linearization to approximate f…

A: Here in this question we need to linearize the given function and then approximate the value of…

Q: Show that F = (2x - 3)i - z j + (cos z)k is not conservative.

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

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

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Q: Thelem:-TP PTR har ociva bveof %eI,theu f is Coutivlalse- at Xo CTs thecouvese of thevem triue?why?

A: Questions from continuity and differentiability

Q: is function oF x $ y xz + y In x = ze-sin (xy) D. Ausumo that z Find zx iF

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Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

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Q: Estimate x using the trapezoid rule withn=4 a. Type equation here. Redo 9 using Simpson's rule. a.…

A: Given  f(x) = x3  a = 0 , b = 4 , n = 4

Q: 2 Find the orthogonal trajectories of r=asin? 0 where a be the arbitrary constant.

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Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·

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Q: Find the analytic function f(z) = u + iv if u = 2 cos x .cosh 2y cos 2x + cosh 2y

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Q: Find the work done for a force F 36 N from x =2 to x =6 m. %3D

A: Here we have to find the work done by the given force on the given interval. Here we use integration…

Q: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: