lim z+y? %3D (x, y) (0,0) | along y = 2x? %3D does not erist 25

Q: Fin d: ) (3x*arctan x do Evaluate: s.) dx

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Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

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

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Q: Tokal dexivetive of f i) Fxy)=In(xy), kind at xzl yal.

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Q: at Solve thie équation use Eulers methoc- ds -t X-ツ dx x+y y(6)%=1

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Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

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Q: (test for exactness) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xyev" )dy %3D

A: Given DE is 2ysinxcosx-y+2y2exy2dx=x-sin2x-4xyexy2dy Test the exactness of the given DE.

Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: n (p hix ( %3D what is the dependent vaniable in

A: Solution

Q: (b) lim (z.y)→(0,0) Vr4 + y3 +1–1

A: limit of the rational function

Q: lim r.y)→(0,0) (4 + (x² + y²) In(x² + y?)) Dose not exist -00 00 1 4-

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Q: ential equati x²y dy = C

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Q: Find each limit f(x, y) = 3x + xy − 2y

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Q: Vhich of the following is correct? A) dx = lim | 1 %3D xp- = lim 4 V.r+4 V.r+4 V.r+4 -2 V.x+4 B) S…

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Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

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A: Given limit, limx,y,z→0,0,0yzx2+4y2+9z2

Q: Use chain rule to find express answer in terms of x only. dx y = Vu² – 1 u = 4Vx

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Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: Exact difterential egation 4. (1+In(xy))dx+ 1+ dy=0 y,

A: Given differential equation is, 1+lnxydx+1+xydy=0   ...................(1) Comparing with Mdx+Ndy=0…

Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: (c) lim v f(x) x→2

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Q: Integrate f(x, y) = y(x² + y°)° over the domain æ? + y? 0.

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Q: f(x, у) 3D 5x2 + 9у2 f(x + Дх, у) — f(x, y) (а) lim Ax → 0 Ax f(x, у + Ду) — f(x, у) Ду (Б) lim Ay →…

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Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

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Q: psen(x) tan(t) dt lim ctan(x) Vsen(t) dt x→0

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Q: Find y' and y". - in(x + V6+ x²) y = In( x + y' = y" %3D

A: Given

Q: a2z Find given that z is a differentiable function of x and y, and xz + yz3 = 2 + x?ev

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Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-²-y²-722

A: In this question, the concept of the derivative is applied. Derivative The derivative expresses the…

Q: dy 1 y? +y 3

A: We have to integrate.

Q: dy for all of : dx Find 3 |x(х-2) 1- y = xvlnx 2- у 3 х2+1

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Q: XY lim メ)→(0,0)Jx2+ y2

A: Calculate the limit using polar coordinates as following:-

Q: y2 f(x, y)dx dy Let f(x, y) = e-x2-y² and

A: answer is in next step

Q: 2. CG X It otx

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Q: ution of yl = x+xy2 W

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Q: lim (z,y)→(0,0) r* + 3y4

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Q: HX T-Th HY 3)1+2 2. 14 the eavation

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Q: e2x tan xy = lim (x.y)- (A) Does not exist (B) e2 (C) 0 (D) e2 (E) e

A: We have to find the limit .

Q: Vx - Jy +1 lim (x ,y )→(4,3) x -y -1

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Explain the difference between t dx dx lim + lim s-0+ dx lim dx +

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Q: valuate dy and A v for v = f(y) = x2 -6x +35 x =4 and dy = Ax= 05

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Q: (3x2y+2e2y+3)dx + (x3+4xe2y-sech2y+2lny-y)dy=0

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Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration

Q: What is an antiderivative of x+2 ? x²+1 x + arctan x – 5 2x + 3 x + arccot x x + 2arctan x + 1

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