Solve of AABC. 2. ABCD is a square of side 6 cm. If a rectangle of length (2x- 1) cm and width (x + 2) cm is cut from the corner A, show that the area of the shaded region is (38 – 3x – 2r) cm². - В (x+ 2) cm (2x – 1) cm 6 cm 5.

Q: 5. The volume of the solid formed by revolving the region bounded by the curve y = Vcosz, I-ax: from...

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Q: = 60 %3D = 30 %D =D3 %3D = ? %3D

A: From the given information,           3 × times of Red flower = 60                        

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Q: (b) Let u = u(x, y) and f and g be twice differentiable functions. Then, a general solution to the e...

A: The objective is to find the general solution u(x, y) .

Q: Consider , xe¬**dx. What will be the appropriate solution and answer to this improper integral? A. l...

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Q: 1 dx. 10. Evaluate the improper integral m 64 + z²

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Q: az dz 10. Compute and for the following equation. dy ,3 eY + xz2 6xy*z³ %D

A: The given equation is: ezy+xz2=6xy4z3...(1)

Q: 0 Use an appropriate form of the chain rule to find dw/dt w = 5x²y°z*; x =², y = t², z = t°

A: As per our guidelines, we only solve one question.

Q: Suppose that f(4) = 4, g(4) = 3, f'(4) = -2, and g'(4) = 5. Find h'(- %3D h (x) g(x) f(x)+g(x) ' Exp...

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Q: 1. Consider the integral | 2nx g(x) dx. There is a function g(x) such that when u = In x the resulti...

A: Given integral is: ∫2ln x g(x) dxsuch that for u = ln x∫2ln x g(x) dx=∫2u duFind g(3) This can be ev...

Q: dz Compute dz and for the following equation. dy e Y + xz² 6xy*z³ .3

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Q: In3 in2 4-ex xp- xV16-Inx 1 x Vinx In2 iv. Ino.5 e2x +1 1 O 2/22 O8-2/15 O 3 2 OIn 2

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Q: f = f (x, y) = u? + 3v, y = uv

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Q: (a) The eigenfunctions of the following eigenvalue problem: X" + XX = 0, X'(0) = X'(#) = 0 %3D are g...

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Q: Evaluate the integral dx 2xx - 3x?

A: To find: The integral ∫dx 2xx3-3x23 Concept used: ∫1-v2+1dv=lnv+12-lnv-12

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x2 + y2 + x²y + 5, D = {(x...

A: The given question has been solved in detail Absolute Maximum value is 8 Absolute Minimum value is 2...

Q: Find the radius of convergence of the power series. (If you need to use co or -0o, enter INFINITY or...

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Q: Solve the differential equation with appropriate method. Simplify final answer the simplest possible...

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1+ x CO f(x) = 1 + -x...

A: From binomial theorem we know, 1+xn=1+nx+n(n-1)2!x2+n(n-1)(n-2)3!x3+....

Q: One of the following is an improper integral. cln 3 e* dx dx J, xV16 – In x In 2 V4 - ex In 2 CA dx ...

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Q: Find the radius of convergence of the power series. (If you need to use co or -co, enter INFINITY or...

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Q: dx 2V x3 - 3x x

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Q: Let f and g be functions that satisfy f′​(4)=2 and ​g'(4)=−3. Find h′​(4) for h(x)=3f(x)−g(x)+2.

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Q: Solve the differential equation with appropriate method. Finalize answer free of fractions and equat...

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Q: 2022" + n 2022 (d) lim sin 2022! + n!

A: We have to find: limn→∞sin2022n+n20222022!+n!. We can take the limit inside of sin as the limit is o...

Q: 2 f(x)dx Given: There is a function F(x) such that when u= -x³, the 2 du resulting integral is Evalu...

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Q: Part of the piecewise-defined function (x – 1) + 2 if 0 < ¤ < 3 f(x) = b if x = 3 mx if 3 < x < 6 is...

A: Given problem:-

Q: Find the nth Maclaurin polynomial for the function. 5x - 1 f(x) = n = 4 %3D x + 1 19 Pa(X) = %3D Nee...

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Q: How many ways are there to represent a function? Find the domain of the following function x²+3x+1 V...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. x) C...

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Q: solution

A: We have to find the derivative of the given function using the rule of derivative

Q: dx The integral can be rewritten as 1- x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī-s) S--0 (c) lim (-2+v1–...

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Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: 2. In each of the following, find fyzz, fryx, fxyz. 2. f(x, y, z) = lIn(xyz) + 2² tan¬'(e"Y)

A: I am attaching image so that you understand each and every step. Note:-  2nd subpart is more complex...

Q: 3-Vz dz 2+yz

A: Power substitution  is a  method of integration that aims to replace the nth roots in a function, wh...

Q: 19-22 Use a triple integral to find the volume of the given solid 22. The solid enclosed by the cyli...

A: Given cylinder is x2+z2=4 and the plane is y=-1 and y+z=4 So,  y→-1 to 4-z z→-4-x2 to 4-x2 And x→-2 ...

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Q: Solve the differential equation with appropriate method. Final answer should be free of logarithms a...

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Q: 11. Determine fuu for the following situation. f = f (x, y) x = u² + 3v, y= uv 33

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Q: A table of values is given for a function f(x, y) defined on R = [1, 3] × [0, 4]. 1 2 3 4 1.0 2 -3 -...

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Q: 7. Determine f (x) so that | cos(In°x) f (x) dx = sin(In²x) + C 2 In x In x (а) 2 In x (c) - (d)?

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Q: cSc x du 5. If u = f(x), then -. Compute f dx = sin x – cos x 2 (a) 1 (b) -1 (c) 0 (d) 2

A: ∫cscxsinx-cosxdx=∫duu

Q: du Form Answer Ssinx Ex. S 3+2cosx -2sinxdx 5(ou -5v3+2cosx + C 3+2cosx 15. Given: dx 3 2sdr a) b) 2...

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Q: Find the Taylor polynomials of orders n = 0, 1, 2,3, and 4 about x = x0 and then find the nth Taylor...

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Q: For the following functions find the nth Taylor polynomial centred around a. 1). f(x) = e, n = 4, n ...

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as ...

Q: dx 3. The integral +1 reduces to where u = f(x) and for some constant k. Compute f(1). (a) (b) e +1 ...

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Q: 22. Determine f(x) so that cos(In²x) f(x) dx = sin(In²x) + C (a) 2 In x 2 In x (b) Inx (e) NIK

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Q: 45-48. Average values Find the following average values 45. The average distance between points of t...

A: Here, the given disk is: R:{(r,θ):0≤r≤a} which is a circle x2+y2=a2 Therefore, the average distance ...

Q: MAT

A: Graphical representation: