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 + zx?, 2)Find p = xz²y

Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

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Q: 327. F(x, y, z) = zi+ xj+ yk; S is hemisphere z = (a² – x? – y?)/2. -

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Q: If f is Caib], ab solute maxinum continouus on then f attains valye fcc) and an ab solute mirinum an…

A: Que: Ans : Given         f(x) is any continews function on [a, b]          Let f(c)  be absolute…

Q: r próducts, šó thát théy indeed. They took an a ts to explore the claim -ies randomly.

A: Let X be the random variable such that the life-length of the battery producer company fabricates.…

Q: The different loul equaticn 5. %3D can be wntten in He torw n He tor m MX, y)dn t N(x,4) dy =0 Find…

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Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0,…

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Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to…

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Q: 12) Show that D. ldi-del is shortest distance bet uleen ax-by+c2di i and ax+by tcz =dz?

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Q: IF d (u,y) is one meter el, prove that on p(a,y) is also one meter on d (u,y) 1 +

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Q: 3 - find the absolutt max. and min. o f the Punction rectangular Plate T = x + xy +y?-6 x O x < 5 on…

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Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: I if é osy =xe, fiel y' by, use Implicite di fferen ional ? %3D

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Q: Which of the following best completes the proof showing that AWXZ - AXYZ? OY Z 2.5 Wo 10 Since xZ 1…

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Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: dy let y = xtan z then is da elect

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Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: 3) Given: SR IRT; TU LUS; 4STR = 4TSU Prove: A TRS 2 A SUT T R U

A: Given, SR⊥RT,  TU⊥US∆STR≅∆TSU STATEMENTREASONSSR⊥RTgivenTU⊥USgivenSU=TRBoth intercept triangle with…

Q: In POR, PRisextended through point R to point S. m/QRS mRPQ = (+ 12), and m/PQR = (3z + 20). Find…

A: Given, m∠QRS=(7x+8)°m∠RPQ=(x+12)°m∠PQR=(3x+20)°

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: 4. Which would not be sufficient to prove AWXZ ~ AWYX? C ZWXZ = ZY WZ A WX XW %D YW XY WZ XZ WX Y WX…

A: In both the triangles angle W is common so for similarity using SAS property:  WZWX=WXWY OR…

Q: Consider the following figure where VA = RV. R A Vhich one of the following tatements is correct?…

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Q: 49. If f(u, v, w) is differentiable and u = x – y, v = y – z, and w = z – x, show that af af ду af…

A: Given f(u,v,w) is differentiable. By chain rule of differentiation , we have

Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

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Q: 6. SS dV に lies b/w ミ 25 %3D and x? f y? + z? Ź 36 in the firót oct ant ...

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Q: Q/D check if The feanction is Contrnous (2 eaisł find if The Cimił es (メリ/→& 0) mn (2 2. x" +3y…

A: (i) lim(x,y)→(0,0)x3yx6+y2 Let y=mx3. Then, lim(x,y)→(0,0)x3yx6+y2 becomes,…

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: m+n If x"y" = (x+y)*** m, n d'y prove that = 0 .2 dx?

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Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

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Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

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Q: R² and r are defined by SR E(*; – T)(yi – ỹ) Say R? SST' r = VE(x; – #)² L(yi – g)² (1) Show R² =…

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

Q: Given: ZW and ZY are right angles WX = XY Prove: AXWZ EAXYZ

A: GIVEN:- LW=LY=90 WX=XY

Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: Nhat is Duf at P(1, 1) if f(x, y) = sin(x - y) and u=i-İ? 3 O 5 O 3 4 O 10 9

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Q: 27. || x sec?y dA, R={(x, y) | 0 < x< 2,0 < y< /4} R 28. || (y + xy-2) dA, R={(x, y) | 0< x < 2, 1 <…

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Q: 4. Evaluat the fellowing usingg Simpson's ţ Fulos hd A-j°x?dx; Aus.(8.667) BaS Z x SAns. (8.7159) .…

A: To use the simpson (1/3)rd rule

Q: Consider the formula A = Vx Vy.p(x,y) ^ ¬q(x, y). (b) Show that A is falsifiable (i.e. not valid) by…

A: We are given a formula as : A≡∀x∀y.p(x,y)∧¬q(x,y) We need to show that A is falsifiable by giving an…

Q: Suppose you wind a thread on a pool of 1 cm. Points K, L, M, N, and so on until S are marked on the…

A: We have to find the length of thread in terms of π.

Q: When two resistors having resistance R, ohms and R, ohms are connected in parallel, R,R, R, +R,…

A: Given: R=R1R2R1+R2 We know that for finding partial derivative of given function with respect to R1,…

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

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Q: aw and ar dw O Find if as

A: In this question, the concept of the derivative is applied. Derivative  A a derivative is used to…

Q: 9. For the cur ve x = t – In t, y = t + In t, find d²y/dx².

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Q: 17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D

A: Let h(x, y, z)=x2+y2+z2-z. We now have ∇f(x, y, z)=(1, 0, 0) and ∇h(x, y, z)=(2x, 2y, 2z-1). Let λ…

Q: Given: ZR= ZZ C R CA= YA Prove: ACRA =AYZA Y

A: Use the congruent postulate and prove that both triangles are congruent.

Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.

Q: 3. If OR 1 PQ at S, mZP = 30 and PO = 12 cm, find PQ

A: According to the Q&amp;A guidelines, one question can be solved. Please repost other questions…