2.) (6x*y+z")² 10

Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

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Q: 7. (4 points) Evaluate the indefinite integral. 5x8 dx = 5x8 +C.

A: integration formula for this question ∫ xn dx = xn+1n+1+C ; n≠1

Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: 2. (i) Show that for a discrete dis.ribution B2> 1. (ii) Show that B2> B1

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Q: Howin If Z=RCxy) and u=xayg V=x-y show that 3

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Q: 7. Determine the integral| 2+1

A: The given integral,    ∫x dxx2+1

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Q: b) Evaluate the intergral. Show (with your work) that it is Cunvergent and give its Value or that it…

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Q: Determine la solución general de la ecuación diferencial Y'-2x/2-x^2(y)=e^x. Y(2)=4

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Q: () = 2 sec(a O conon1 O pton 2

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Q: 5. Triangle JKL with verfices J(1,-1). K(2, 3), and L(3, -2): x=4 J': L': K'

A: In the question it is asked to take a mirror image of triangle ∆JKL about x=4. Coordinates of…

Q: -25 Evaluate the integral: dax x²Vx2 +25

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Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: 4.3 Use the calculus of residues to evaluate the following integral (x2- dr. + 1)2

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Q: 7. Show for y = u.v that y"= uv"' + 3u' v'" + 3u" v' + u''' v.

A: The detailed solution is as follows below:

Q: 8. Express as a polynomilal. Arrange your answer from term with highest degree to lowers degree *…

A: SINCE YOU HAVE ASK MULTIPLE  QUESTION IN SINGLE REQUEST. SO WE WILL BE ANSWERING ONLY FIRST…

Q: 3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then…

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Q: Prove H'n(x) = 2nHn−1(x), n = 0, 1, . . .

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Q: 12 Integrate: ,V4 - z² + dr

A: The given function is 4-x2+x7+24-x2 We have to integrate this function over the interval -2, 2

Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

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Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: 74. Show that if 0 < x < y, then Vỹ - Vx < Vy – x.

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Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: (a) through the midpoint rectangular rule and (b) through the trapezoid rule. Discuss your results…

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Q: Verify Young's Theorem z = In(2x + y) -

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Q: If y = xsinx then prove that y''+y=2cosx

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Q: 3. Prove the pythagorean Theorem

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Q: Еxercise 13 Determine how тany times 0 арpears in thе тultiplicatioп table for Z16-

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Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: 10. Triangle JLM with verfices J(-5, 7), L(8, 3), and M(-3, -1): (0, - 5)

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Q: (4+38)-(9 -J2) Rectangular ?

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Q: I need help doing number 7

A: We start solving the given equations simultaneously.

Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

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Q: 16) 1. ZDX 2. -X Show Your Work Valid Invalid

A: We have: Z⊃X~X ∴~Z    This can be written as Z⊃X∧~X⊃~Z  Here, p⊃q means "if p then q" This argument…

Q: 4. Sketch the proph of the following funcfions; メーメ+4 (x+4 a) f(x) = (x+4) x b) gex) = %3D

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Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: 8. S(1- sec3x)²dx

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Q: 6. Use the IVT to prove that x2+ In r = has a solution. %3D

A: The Intermediate value theorem says: If the continuous function attains two values then it must…

Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

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Q: HW.12 Describe in your own words, what is Limear tram furmatim" How the' concept of meant by n…

A: Linear Transformation:      A linear transformation of matrix is changes the original value to the…

Q: 4014H al

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Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: What is thie generalized union and interdection of %3D where 1-10,1)

A: As given,  λ is the index set for A.  Hence, there are two sets possible,  Aλ=0  =  [ -(1/0) ,  0]…

Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…