Evaluate / (x* – 2y) dA where D = {(x, y) E R²| – 1 < x < 2 and – x² < y < x²}. -

Q: 3tan z sec? x dr 2.

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Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

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Q: If f(x,y.z)= In(x2 +y³ +2z5), Find and dx² dz2

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Q: ス+)V2x+x dxメ

A: Given,          ∫x+12x+x2dx

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/escx))

A: To find the y"+3y'×5y at x=5  Given y=xsin(1/cscx)

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: Calculate the LOS of y = -x² + 4 LOS is x = a is b is c is

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Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

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Q: x^2=Axy+By

A: Simple value put

Q: (b) Differentiate (Vx+ 1) with respect to x. 2/3

A: as per our guideline we can solve maximum one question you can repost other questions

Q: Find yll of x³+y²=3 by implicit ditferetlal C1o pants

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Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: Let_y=x² +5x³-4x+1 then dy- ||

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Q: 2. Differentiate the follow a) y = e 2x -ex %3D ex

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Q: (a) x² + zsen xyz = 0

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Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =…

Q: 5 Use implicit derivation to find y. x² +y +z =e"-

A: Given,           x2+y2+z2=exyz

Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: What is the DE for A(x^2)+Bx+C using elimination of arbitrary constants.

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Q: rsin 28x /ī+ t² dt and If f (x) = So g (y) = ' f (x) dæ., what is g" (6s )? 168

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Q: Solid inside x2 + y2 + z2 = 16 and outside z = √x2 + y2

A: Given:

Q: what is the antiderivative F(x) 0f f(x)=3x^((1)/(2))-x-1that satisfies the condition F(4)=0 A,…

A: Given that:f(x)=3x1/2-x-1, F(4)=0

Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

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Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

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