Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

Q: 1.n f csc n? de y2 - 2y + 3 2.5; Vy - 3y: + 9y – 21 dy

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Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

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Q: 1. Find 2(3z + 4)² dz.

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Q: Determine the length of x = 3 + (y – 2)² , 4 <x< 19

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Q: 8) 2x+5y=5 x-4y=9

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Q: Solve for A. ЗА t3D A =|

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Q: (In æ)" Find y'. Let y = e" + 2

A: Explanation of the solution is given below...

Q: ework: dr if r= Vs+1 and s=16t – 20t. dt Find |

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Q: Suppose k = 0,1hr−1 and T = 10hr. Find the smallest n such that Rn > 0,4R.

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Q: 22) S, S** xdydx=? А. 1/3 В. % С. 3/2 D. 5/6

A: The given integral is ∫01∫0x+1x dy dx

Q: Exatuate the integral QUS √3x xام واح

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Q: W Solve P = for t

A: Given query is to solve for t

Q: Suppose that two nondimensional quantities are exactly A chapter, express the four quantities (A+B),…

A: Given,          A=8.73       3 siginficant figuresB=1.389     4 siginficant figures

Q: ∫(5e5√y/√y)dy That is 5e to the (y to the 1/5)

A: We have to find

Q: h zp dy +6. +9y= dx² dx r²e-², 2

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Q: You are designing a spherical tank to hold water for a small village in a developing country. The…

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Q: Use simpson's '/3 mile to numerically From 0 to Tu. Show your solution : 14 12 Xo:6 f(x0):8 f (x₁)…

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Q: bläi 6 Q/ By using substitution z=x+y to make the D.E. dy/dx=(x+y)^2 separable :equation, the…

A: The given equation is; dy/dx = (x+y)2 and substitute x+y = z.

Q: 4x -1 b) dx. J x(x? + x – 6) c) xV4-x² dx.

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Q: 2 3/2 What is the value of √ff e(²² +3²+²²)³½³ dV, where B is the unit ball, x² + y² + z² < 1? 4 π…

A: Step 1:​I=∭B​e(x2+y2+z2)3/2dVB is the unit ball, x2+y2+z2≤1​Step 2:​Using spherical…

Q: Q6:-Find aw and ar if as 1) W = x2 + y² 2) W = Ln(x² + y² + 2 ,x = %3D

A: It is partial derivative

Q: a) Find the value of + 1) tdt by using the substitution u = +1

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Q: 1. Solve for the variable x. F = kx – kxo A. x=F-kxg А. х- O B. x=F-kx, k F- Kxo О с.х3 C. x= D.…

A: The given equation is F=kx-kx0

Q: f(x)=Vx+10 X-4 Damain af flxt Donain of fle(x)) =

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Q: Solve v=m/4(a+K) for K.

A: To Determine: solve for k given: we have    v=m4(a+k) Explanation: as we have 3 variables so we will…

Q: Solve the IVP By LT

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