Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

Q: 2. Find 02z дхду for z = x2 tan-1 Y X

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Q: Q5) if z = 1./(3+x.^2+y.^2), where x and y = -3:0.1:3, could you plot x,y,z as shown below: 0.3 0.25…

A: Given: z=13+x2+y2where,x=-3,y=1.3   Now plot the given function.

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: Q4) Choose correct answer : rtan-(cotx) dy dx = i) So 10n а. 44 15n b.- 44 20n С. 44 d. 1-n 2

A: Given: ∫01∫0tan-1cotxdydx

Q: *csch(2 sin 2x)cx 1. V1-4x let u= du=

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Q: Let C z-1=3 and1 = §, = dz. Then

A: The solution is given as

Q: Compute : csc(e) d Csc evx dx CSC - Csc cot evx А. 2/x B. csc cot(evF).eF . — cSC Cot csc · cot 2 D.…

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Q: Find tan a. V[ ? (V5, -/7)

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Q: OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv -…

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Q: 2) 3. | 24 ly-11 dy

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Q: dx tan x -1 '+ 4dx de x- Vx

A: Taking #5 and #6 As per authoring guidelines, if the question number is not specified, the first…

Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: The graphs given are as follows:

Q: Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w v2 fuu + u² fov – 2uv fuv - ufu - vf dx2

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Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

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Q: У(2x? — ху + у?)dх — x? (2х — у)dy %3D0;B у(1) - H IN

A: Use homogeneous equation

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

A:

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: A 4,-1) B(4,-2) find lime x approachesto1 from postve dinection.

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Q: (5a.4) dn 1 (2,2) (a?-x +1

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Q: If V2 1 1 dv = x V2 V1 \V¼ V½) V2 Зпх -dv =? 1 2T7(V + ny) V1

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Q: Q2. If w = f(u, v) , u = cosx and v = sinx, show that: (30 Marks) d?w = v? fuu + u² fvv – 2uvfuv –…

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Q: Hw/ sketch f(x) =-2*

A: According to the question, we need to graph the function. The function is given as : f(x) = -2-x…

Q: find Pn (Q'U R).

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Q: 4 V = Tr. Find V'. 3 V'

A: Given the volume is, V=43πr3

Q: Evaluate : p.v x2 ∞ (x²+3)² dx

A: To evaluate: p.v ∫-∞∞x2x2+32dx We will evaluate the integral using Reimann integration.…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.