Ex6: Find for the foll dx a) x² y? = x? + y? 2 X-y c) - = 2 at P(3,1) x-2y Sol:

Q: Q4) Find the deviva tives of the follocoing (9) y = ( In xe) %3D (b) Sec ( ²+1 %3D

A: Part A -  We can observe that the power in the expression on the right-hand side contains the…

Q: What is -4y dx + 2x dy, where C is the circle „² + y² = 16? O 967 O-167 O-327 O487

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Q: Use these 3 methods to approximate , ex dx, n = 8 a. Trapezoid Rule b. Midpoint Rule c. Simpson's…

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Q: Ex. Evaluate ff y ds where S is the portion of the cylinder x + y = 3 that lies between z= 0 and z=…

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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: f (x, y) = 3x2 + y + 4xy + 8 %3D af(z,y) when x = 2 and y = 1? dy What is the value of %3D

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Q: Apply Uptimal obtain y, y₂₁ and y for the pr 3

A: given y'=t+2y h=0.1 and y0=1 to find the y1,y2,y3 proceed as follows Apply Runga Kutta 2 order…

Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: Use the trapezoidal rule to find AT using the indicated value of n. 8 dx; n = 8 2x2 +2

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Q: SS * dydx, y In x Where R is the rectangle 1 sx s e,-1sys2 Calculate

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Q: E is the portion of the ball x +y +2 s9 that le NOTE: When typing your answers use "rh" for p. '

A: We have to find the following given conditions according to the given information

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

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Q: d?F – AF = 0, dx? slove avec F(0) = 0, F(1) = 0 et aeR.

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Q: Find a solution of x dy =y?-y that pases du Through indicated points

A: For the given problem, below is the solution.

Q: Evaluate O y°dx – x*dy, where C is the boundary of the region between the circles a? + y² = 4 %3D…

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: For a function y(x), the quantity dydx represents the first derivative of y. This quantity…

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

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Q: S is the midpoint of RT and U is the midpoint of TV. If RV = x + 7 and SU = x, what is the value of…

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Q: ∫C  ez / (z - πi) dz where C is defined as z(t) = 2eit and 0 ≤ t ≤ 2π

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Q: Please evaluate P (3y – esin(@)) dx + (7x + Vyª + 1) dy, - where C is the circle x2 + y? = 9. Hint:…

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Q: C. uoing Separahion af variables, find_the general 'solu ton of the given' D.E. dr = bCcoLedr +rsnt…

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Q: Frd he e of teepkan in the at quectert baurded on he let ty he ydx, bebw by tte carve x- boletby…

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Q: Eхample : Evaluate the triangle fxy dy - y? dx around the square cat from the first quadrant by the…

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Q: R is the midpoint of QS and T is the midpoint of SU. If QU = z and RT = z – 43, what is the value of…

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Q: r cot VE-tan° V cosº /T VEsin JE dx

A: Given that: ∫cot3x-tan6x.cos6xx.sin3xdx

Q: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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Q: Evaluate tot? xe*< + y2 + 22 dv, where E is the portion of the unit ball x2 + y² + z2 s 1 that lies…

A: Triple integral

Q: FOR SET AND SOLUE 2 Y=x y =X S S x?y dy dx AND R R YOUR ANS WERS SHOULD AG REE.

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Q: The reverse order of f, S, sin y² dydx is f, S sin y? dxdy False True

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Q: Given f(x, y) = 2a° + 5æ?y – 3y?, find %3D f-(x, y) = %D f,(x, y) = %3D fza (t, y) = %3D fzy(t, y) =…

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Q: Hw I show that' O div (fog) =Pa'g + oP.ug e cur (f) = 0 where

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Q: 3. In the diagram below, AB = BD = 5 and AD = 7. %3D %3D Is BD tangent to OC? Explain.

A: Given,      AB=BD=5 and AD =7 We need to explain is BD tangent to C?

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: arctan dA , where R = {(x,y)|1< x² + y? < 8, 0<ysx} %3D

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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: fro assoc е топоwing probat df = 8, P(t 2 2.306) give degr с. df%3D21, Р(—1.323 <1< 3.1

A: We are authorised to answer three subparts at a time since you have not mentioned which part you are…

Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: Evaluate : dz where C is the cirlce z – 2=1.5. 8 Ti 4 Ti -8Ti |

A: Residue theorem: The function f(z) is analytic inside a contour C except at z=a then the integral ∮C…

Q: Given that f(t)dz what is 13 f(s)ds? 11 enswar

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Q: Expend flx,y) stan' (")n pow ers 6f Cyリ Up to third clegree torms. Hence, Com pute f(1., 0.9)…

A: Given: f(x,y)=tan-1yx

Q: D Given: l, m antersect at P M <1 = 2x+5 m22 = X+5 %3D Pove: x= 50°

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Q: 7.) Find r'(t), r"(+) , r'(t) · r"(+) and r'(+) x p"(t) r(+) = +*-at) +우 %3D 2 9. a.r' (t) = ? %3D…

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Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

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Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: m FGH F リ to H. m FGH = %3D

A: Given  Circle having center somewhere at Fh. To find the ∠FGH

Q: If Jf(x)dx = cotx? +C, then f(x) is equal to

A: ∫f(x)dx=cot x2+C

Q: Determine the order of the DE. а) y' + у %3D 5у? b) = t dy dt c) y' = y" + 5t2

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Q: Ex Find the Salution of the sliff. equ. + 2x° cosx, given that yf z dx

A: Here we have to solve differential equation