(c) Suppose that o is differentiable. Prove the identity | øVø •n ds : (OV²ø+ V¢ • V¢) dA

Q: e*, when 20 = -1 %3D P„(x) sin(nrx) – nn cos(nax), when 2, = (nx)² for n = 1,2,3,.... a.) Show that…

A: Hi! As the questions are lengthy, we are answering only the first subpart. If you need an answer to…

Q: Find the onthogonal trg ectories of y(sy +c) = I.

A:

Q: S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

A: Given that, f(x, y)=sen2r2-θ2+lnrθ+θfor r=x2+y2and θ=arctanyx

Q: Using the Green's 2nd identity, prove that for 2-D Neumann exterior problems, O(In r) 09 Inr-0 dl .…

A: Consider the Green's second identity, ∭Du∆v-v∆udv=∬∂D=u∂v∂n-v∂u∂nds From the equation consider the…

Q: If f(x,y,z)=sin(xy)+x2lny, then fxy at (0,pi/2) is equal to 1 FO

A:

Q: If z = f(x, y), where x = r cos 0 and y = r sin 0, show that a²z 1 a°z 1 əz r дr дх? dy? дr?

A:

Q: By using the residue theorem, prove that 1 dx 4a3 where x E R, and a >0 is a parameter.

A: Given

Q: 3. Use the theorem in Sec. 48 to show that (z – zo)"- dz = 0 (n = ±1, ±2, ...) when Co is any closed…

A: The given question is solved below.

Q: Given that F(x, y, 2)=sin xi+ cos yj + xzk. Evaluate F.dr where C is given by r(1)=(r.-r.1) : 0SısI.

A:

Q: 1 Evaluate J JA Totu2)2 dxdy, where A is determined by the conditions 1< x² + y? < 2.

A:

Q: Prove that the following ODE IVP is well-posed: where f(t, y) = 1 + t sin(ty). y' = f(t,y), 0< t <…

A:

Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

A:

Q: 2- find ow/ar if w = (x + y + z)², y = cos(r + s), at the point (r, s)=(1, -1) x = r - S, z = sin(r…

A:

Q: What is f 2sm z cos e sin x dæ? 2sin z +C In 2. 2sin z +C In 2 2cos z +C O A. O B. In 2 20os z +C D.…

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: EX show that J, (x) 2. sin X %3D zm + Sol:- J CX). = (-) M=D0 m+ LIN

A:

Q: If f(x, y) = cos (xy) – 7y, then fx(0, x) = 0. %3D Select one: True O False

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…

Q: garded as a subset of R. 9.E. y ing theargme ang ), prove that the interval J = { (x, y) : 0 < x <…

A: 9.F  We have given J=(x,y):0≤x≤1,0≤y≤1   to prove the compact in R2 we have to show that J is closed…

Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

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

Q: How do I prove this?

A:

Q: J prove that for 0 <r<R

A:

Q: Suppose h(z) is analytic at z = 0 with h(0) = 4, h'(0) = i and h" (0) = 2 Compute the following…

A:

Q: E/Prove the foltowing Eoshtutv)= CoshucoshVt Sinhu Sinhk

A: To prove that cosh(u+v)=coshucoshv+sinhu sinhv

Q: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

A:

Q: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate w when…

A:

Q: 2 Evaluate the fullowng cartesianntegrat changing theminte equivalent Pelarintegrals: Fー dxdy 2-

A: We have to find the double integral using polar coordinates.

Q: (-1+i/3)°, by using deMoivre 's theorem

A:

Q: 12. Evaluate by using Stoke's Theorem [sin z de - cos x dy + sin y dz] where C is the boundary of…

A:

Q: Find b∈R such that ∫∫Ssin (b) ydS = 8, where S is the part of y^2 + z^2 = 4 that is between x = 0…

A: To find the value of b satisfying the given integral.

Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

A:

Q: 14 Jlgull s(e)= f(2) =Re z is continuous ylgn O Ihs O

A:

Q: R Given: RT = QT, AT = ST A s, Prove: AQSTARAT

A:

Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

A:

Q: Let C:z-1 in the counterclockwise direction and/- dz, J = $ Lnzdz, and K-4, tanždz For which…

A: We are asked to find where the Cauchy Goursat theorem applicable. So, first we state the Cauchy…

Q: Let f(x, y, 2) = eF tan(x² 2) . Compute fay: (x, Y, z) . Simplify your final answer.

A:

Q: lim, ,0* Sõ sin(t*) =? O a. 00 O b. 1/3 O.c0 O d. 2/3 O e. Limit does not exist е.

A: The correct option is, option (b), i.e. 1/3 The detailed solution is as follows below:

Q: 1)the f a) 3 cosh z b) 0 c) in d) n -dz by using the residues is equal to

A:

Q: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

A:

Q: DG DH Given: DE ZDGH = LE DF Prove:

A: Consider the figure with given: DGDE=DHHF. Prove: ∠DGH≅∠E Consider △DEF. Apply theorem- If a line…

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

A:

Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: Considere a função z(x, y) definida implicitamente pela equação sen(y - bz) = -2+x - az, com a e b…

A: (i)

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

A:

Q: R Given: RO = SE, RO || SE Prove: ZR LE E

A: First, we will show two triangles congruent .

Q: What additional information would you need to prove ATRO = AMT by the HL theorem? A TR TM R В ZOTM 2…

A:

Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

A:

Q: 1 (aw C. Ifw=f(x.y) and x=1. coso, y=. sino. Prove that

A:

Q: State De Moivre's theorem and if z 7+ j4, find z5 using the ( theorem.

A: Given query is to find the value of z5 using De Moivre's theorem.

Q: dy +. (x>0) tind the Soiution of the difperential equation, expressing 4explicitly as general 4…

A: First we comparing the given differential equation with dy/dx+Py=Q .and then find I.F. and then…