find the anti- deriva tive of the fun cticn: fcx) = 4 cSca cotx - Secx cot x

Q: find An eignuector of the matix 12 17 2 VZ V3 19 2 J3 -VIT -2 Ji

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Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: find the funotion with hejp of a indegral meau value betw een 4,1] of g(x)=\xl-2

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Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: is con hinuous neither in the in ter val [o,3], piecewise Determine if the funchion continu ous 3-t,…

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Q: "he pmf of X is 4.x – 1 - fx(x) = where x = 1, 2, 3 %3D %3D to

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Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

Q: Find the family of orthogonal trageclarnes fo he for

A: Given that            y3 = k x5 Here we have to find the family of orthogonal trajectories to the…

Q: If f(z) = cosh(In z“), then f' (7) = %3D %3D Your answer should be rounded to the nearest whole…

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Q: Given the mife has betweeu so oud $ 50,000 of msurauce what ios s the ebatily probabii tū between 0…

A: The conditional probability formula is, PA|B=PA∩BPB The row totals and column totals are,   0 -…

Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: most consiolera Hon when subiects? Whet is he Impor tont designing on humen

A: In a county, people are very important other than living beings. The human population plays an…

Q: (b) In(2x2 + у — 23) %3D х

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Q: Show that J74) LOSK +Sinn 2. %3D TIX

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Q: Again differentiate with sespect do 'x get we A cost- B Sinz A cosz + BSiny) { from @ d +

A: Please refer the attached image for complete solution.

Q: Suppose n is an integer and z-z3D =r is a contour traversed n dz %3D once in counter clockwise, then…

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Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: Prove that d (sec"x)= 1.

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

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Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

A: We have to show that x of x is the distance from x to 0 Hence, x can e written as x−0 x=x−0 The…

Q: △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove…

A: Given △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1)

Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

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Q: The Position of by Patticle defined (4Sın TI ti+4costj + 6tK) Determine To magmtude of velouty and…

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Q: Inand consicr HeLines (tn) venfy Al-5,-6) isapoint of (d) 2) prme Hat (4,)-b de] 3) Cans tract (d1)…

A: Since your question contains multipart, we solve only 1,2,3. If you need any particular question…

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: ind the points sharizantal. Lemniscate » 2

A: Given:The equation of the lemniscate is 2(x2+y2)2=25(x2-y2)To find:The points are the…

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: Let z = 6exv , find dz %3D

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Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

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Q: /show that fo-1x is-Contindals everywhere.

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Q: Considere a função z(x, y) definida implicitamente pela equação sen(y - bz) = -2+x - az, com a e b…

A: (i)

Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25

A: Note that left half of the circle x2+y2=25 means the second and third quadrants. Now, in the second…

Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: What theorem shows that GTY = GUX? Osss O SAS O AAS O ASA

A: We have to check

Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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Q: l? sc tue suell metuozd to fired tue voune of te Solid genented the by rerolning the plene rgim…

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Q: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

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Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.