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Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

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Q: 2+ex dx ex Evaluate:

A: Topic = Integration

Q: Differenticte y= (SN( 3))/ (4t 5cos (2x))

A: Given :y=sin(3x)4+5cos(2x)

Q: I was wondering how the number for pi/4is not sq root of 2 over two ike unit circle

A: topic - rationalisation Rationalisation is a process by which radicals in the denominator of a…

Q: MERA If A- Ga b.cidi and B=9 esfi9s is R=9(0; e) casf) (a,9) (bie)(bif) %3D ffom support your answer…

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Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

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Q: 5) [9*dx

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Q: et = 8 M8 n=0 en n!

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Q: Find indefinite intrege ex -2e て +)S =xp ( xe

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Q: Hoist meihanism with a colera tion finu dis Plucement *こV1+o.256 ;PVニomis Sz3m for もこos and…

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Q: sechx+cshx b) prove that e2x cshx-sechx

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Q: derivatma ofy= ff) -glglw)

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Q: Inn NTT <os 2. n=1

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Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: 6 uoi ion V 108r²y³ +xv/ 75y³

A: We have to simplify   √(108x2y3) + x√(75y3)

Q: The differential equation that represent the following syster 1 -1 x, is 2 3

A: The given system is, This system can be written as, On differentiating equation (2).

Q: b.) show that brnormal of the muolute the unit *-ズ+(c-s)で g =dG) |k-s) K| K* where K is the…

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Q: d. y =x (n* + e*)6

A: Given that, y = x (πx + ex)6 And we have to calculate the differentiation of the given function,

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A: Here we will use the ratio test for convergence of series

Q: Prove tuat fsecodo-On/sece + tanco

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Q: UsxこUt UCot)< u(Sょ) =0 ucx,o)こX separation of V ariable methsd

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Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: 33.) Show all steps to evaluate by hand: 4-х2 Vx2 + y2 dy dx

A: We have to evaluate the double integral using polar coordinates

Q: Q9) In University of California among the placement cell, P(students getting placed )=2n/9,…

A: P(students getting placed)=P(students not getting placed)=

Q: Enter an expression into each box to create

A: Here we have to fill the box.  20x+=5(+7)

Q: Let X- N(10, 5'). What is P(X > 3)?

A: Provided data are,

Q: As PQR in sicle Circl 2²4²25 Such that & & Rone (3,4) &(-4,3) fmd <Q PR?

A: Given that PQR is a triangle, which is inside the circle  such that P and Q are (-4,3) and (3,4)…

Q: Suppose that Cov(X, Y ) = 5. What is Cov(3X + 4, 9Y )?

A: Cov(X, Y ) = 5 &amp; We have to find Cov(3X + 4, 9Y )

Q: 03)Find: T(n+1)% = 1) 2) 3) T(e)= %3D

A: 1. From the definition of gamma function we know that τ(n+1) = n!

Q: =] Verify n(n + 1)(2n + 1) 6 j=1

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