Let C: z-il=3 and I = $. e 3z dz. Then |=0 O I= 6ni None of these |= 4ti

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A: Given query is to find statement is true or false.

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Q: Express dw and ds interms of rand s, where w = x2 + y?x = r – and y = r +.s = 5rand w as = 38 4rsand…

A: topic - derivatives note : As per bartleby guidelines, we are supposed to answer only first question…

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A: you can clearly understand if you follow the below solution

Q: Let C: |z-il=3 and I = $. , dz. Then e 3z z2 |= 6ti |=0 |= 8Ti |= 4Tti None of these

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Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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

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Q: Let z ax y + bx'y?, with a and b constant. P is a point given by (1, 1) and it is known that az (Р)…

A: Solution is written in below steps.

Q: Let C: z-i-3 and I = 4, dz. Then %3D |=0 |= 6rti |= 8ti O I= 4rti None of these

A: third option is correct

Q: 4. Given that T : R² → R* and is defined as T(x, y) = (x + a, y + b) . Prove that

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Q: Let z = a?y- ay?, x = e-24, y = e*, then which of the following is at O a. 2e-2t – 2e2t O b. 2e2t –…

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Q: Let z = ety, where x = Vuv and y . Find dz in terms of u and v.

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Q: aw b- if w = x + 2y + z2, x , y r2 + Ins and z = 2r , find the value of ar .rk)

A: We will solve the following

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Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: Q5.Given that W = f(x.y.z)% x+2y+, find : aw aw in terms of s and r, if and x=, y=r +Ins, =2rr.

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Q: How do I prove this?

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Q: Show that d(y,u)/dv = (1– v²/c)3? for y, = 1//1- v²/c?. %3D

A: Given: γv = 1/1 - v2/c2

Q: Let C: |z-il=3 and I = f. 22 e3z dz. Then %3D I=0 |= 4ti |= 6i O I= 8ni O None of these

A: From the given problem:   I=∮e3zz2dz   So, z2=0⇒z-0z-0=0   It means that poles are: z0=0 &amp; 0.…

Q: 198). Let c be (,0) to(4r, 0,0) G=) ydx+ xdx t Xyz dz Is 6CX Y,Z) independent of C?

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Q: Let A = {x E Z: 8lx} and let B={EZ:12lx}. Then None of these ВС А O ACB O A=B

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Q: if x? + y? = 4 then prove that = d'y dx %3D

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Q: a2u 1 du 1 a?u = 0, ar? r dr (r,0) = 0, u(r,t)= 0, 0 <rsland u(1,0) = 0 pour 0ses %3D

A: Given,                  ∂2u∂r2+1r∂u∂r+1r2∂2u∂θ2=0                             (1)with u(r,0)=0,…

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A: Using polar coordinate evaluate the above integral

Q: Show the following differontial quahion is hamegenous and Solve it: X*dy +C y-xy) dx

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Q: Given that A det(A) with det (A) + 0, consider the following statements: -67 d () aet( A) detaj…

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Q: Find where . Vg r = |7| y g(r) = In(r") si = xi + yj + z 1) to be If you know that Vp x V¢ p = 3xy +…

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Q: Which condition would prove AJKL AXYZ? K Y 7. 56 7. O A. JK XY %3D B. JL XZ 8. C. KL YZ 8. O D. JL…

A: The given sides are, KL=56  YZ=7

Q: Q/ If the joint p.d.fof X and Y as f(x,y) = }*y (cx?y ,x2sys1 ,0. W find the value of c and P(x 2…

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Q: 2 If V) 3 ли?h +- л , where h %3Dh() and r e R, then V'(1) is A. 2ærh -r'(1) + Tr² · h'(1) +27r² ·…

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Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: Let C: |z – i| = 3 and I = $. e 5z dz. Then 22 %3D |= 4ti |=0 |= 6ti None of these |= 10ti

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Q: Ex: Find and . fie 28. u = rs? In t; r = x², s = 4y + 1, t = xy³ %3D

A: ∂u∂x and ∂u∂y

Q: Given f(r, y, z) = In(x² + y? + 2²), show that af, f, s dy? %3D dx² x² + y? + 22

A: The given function is fx,y,z=lnx2+y2+z2........(1) To show: ∂2f∂x2+∂2f∂y2+∂2f∂z2=2x2+y2+z2

Q: Q5/ If w = f(x,y),x = rcos0,y = rsin0 show that: af af 5² + 1 dw Əw. -)² + ar r2 a0 дө

A: The chain rule can be used to calculate the derivative of the complex functions. The function which…

Q: Let w = 4x? + y? + z? x = psinpcose y= psinpstno z = pcoso Find dw dw dw de ee de

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Q: az az Q1/ a. Find and if z= (x² + y²) where x =r+ e*and ar as y=Ins

A: Solution: The objective is to find the partial derivatives of the given equation

Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: The identity S dyd x f, dxdy is %3D O False True

A: We need to check whether the given Identity is True or False.

Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: If C is given by x(t)=t,y(t)=t,0sts1, then S. | t?dt. xyds = Select one: True False

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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 be Z= ax? yf +bx²y³ 9 and b que cors P is a pant givon by (-1,-1) qnd we Anaw dz (P) = -2 , &르…

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Q: Let a A =| d e f h i and 2a 2b 2с B = 2d 2e 2f i Given that det(A)=1/12, what is det( B-)? Answer:

A: Other

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer

Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.