Exercise 4. * Let f(z) = sin(3z) and C: |z| = 1. Then fe f(z)dz = a. 0 b. 3ni c. -6ni d. None of the above

Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: Determine fry when f (x, y) = x sin¬' () -1 1. fry = (x² – y?)3/2 y? x² – y? 2. fry - xy 3. fry (x²…

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Q: Consider f(x,y) = cos(x² e³). Then which one of the following is correct O!. fx(x, y) = – 3 y² sin(3…

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Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…

A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t  and z=1t To express dwdt in terms of t

Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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Q: (a) if f (t) = te“ cos 5t then L{f (t)} =?. %3D 4s2 + 19s + 52 (b) if F (s) then L-1{F(s)}=? %3D s…

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Q: 21. xe2x cos x dx (Hint: Let u = x*) %3D

A: The integration by parts method to integrate the product of two terms u and dv is given by the…

Q: If f(z, y, z) = sin(z) +ay2-23 then the value of a that makes div(Vf) = -sin(z) - 6z is Answer

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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…

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Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: Exercise 3. * sin(3z) Let f(z) and C: |z – n| = 1. Then S. f(z)dz = z (z-n) а. О b. 2ni с. — 2лі d.…

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Q: Determine the general antiderivative of the function. n (x) = cos(5x +1) . True or false? N (æ) = –5…

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Q: 2. Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a.…

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Q: s gluai 2 si x = vt +1 ou y = 2xcosx + tanx? as il l J mal (x sec?x? + cosx – x sinx) (1 VE+1 1 (x…

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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" –…

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Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: 1. If we are trying to evaluate thef esinx cos x dx, which substitution would be most helpful? А. и…

A: Select the correct option?

Q: Graph the following vector fields

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Q: 3. Why is u = cos x, dv = x dx a poor choice for evaluating | x cos x dx?

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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: H.W: if w x2 + y2 + z2, x= e*Cos6, y-erSin0, z=e0 prove that aw/ar= er/w and aw/a0 = e20/w

A: I am going to solve the given problem by using some simple calculus to get the required result of…

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: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

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Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: Choose true or false of the following 1- S, x? = 1 2 %3D 3 2- J sin x dx = 2 3- Se* X² dx = xeX + c…

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Q: 2. Given that z and w are independent variable and dependent variable dz respectively, obtain dw a.…

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Q: (i) Let f(x) E[an cos(n7x) + b, sin(nax)] , %3D where, | +x, -n <x< 0 | 0, f(x) = 0 < r<T. Then, b,…

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Q: Evaluate [P F = (4%, F(t)= (t, sin(t), cos(t)), 0≤ t ≤ T F. dr where 3y, 2x), and C is given by

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Q: az Find when u = 0 and v dv 117 if z(x, y) = sin x + cos y, x = u •v, and y =u + v.

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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

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Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: What are the values of and cz so that y(x) = cq sin(x) + c,cos(x) will satisfy the conditions y(0)…

A: Given y (x) = c1 cos(x) + c2 sin(x)and y(0) = 1,   y'(π) = 1

Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: z{cos (: -)u(: - )} = a) 3 3

A: We find the given Laplace transform. Formula:  L{cos(at)}=s/(s2+a2)......(1)…

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

A: u=x2cosy+yexyx=s+2ty=st

Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: (a) Calculate aw aw and using the following functions: - ди av х+2у — 42 2х — у + 3z w = f(x, y, z)…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: dy when (cos x) = (sin y)* dx A Find %3D

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

Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

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

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Q: az dz A. If Z = ey sin + ex cos then show that x + y ax = 0 dy B. If f = x?cosy + y²sinx then show…

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Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

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Q: 1 Use the substitutions given to find fI+x dx; u = 1 + x + sin x dx; u = sin x cos x a

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