Which theorem can be used to prove that ΔROM ΔΡΜΟ M P.

Q: (a, o) is not measurable.

A: to find that a,∞ is measurable or not  proceed as follows We know that every interval is measurable.…

Q: 1 Prove that 3 dx s VI VI

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Q: Given that tan² O +1 00|m O ± IN 11 8 000 = 100 8S 3 8, what is the value of sec e?

A: I have stated the used formula in the solution.

Q: Sketch the graph of the function and express the function in terms of the unit step function, u.lt).…

A: We will find out the required values.

Q: c2π 0 cos 2t 17 - 8 cost dt

A: Cauchy residue theorem is used to find the integral of a closed curve. Cauchy residue theorem says…

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 day) = So, x** 0₁ X=Y. defines a metric on X₂

A:

Q: Show that S COS TX 2x - 1 dx KIN ㅠ 2

A: We transform the integral into another well known integral and then evaluate it.

Q: [2 1] Q2) Assume A = |1 3 L3 4] [2 4 6 4] ㅋ 4 and B = 13 show that (AB)' = B' A'

A: Solution: The objective is to show that the given relation

Q: Find the value of the Conj uction g(+) ifya know that w(f.g)=3e" and fCo=et (Wronskain)

A: We will find out the required value of g(t).

Q: a) Prove that, a dy [r² √а4-y4 4а√2π

A: Since there are more than one question, so find the solution of the first question.L.H.S.=Let From…

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: e) fsin' xdx fcos"a 4 3x e

A: Given, (e) ∫sin2x dx   (f) ∫cos2x -4e3xdx   We have to integrate .

Q: | a 0.24) tan(sin-1x) = b) c) =x d) 1 - x2 3

A:

Q: Suppose that fex, & C² [0, 1], fixo Lo at f fox dx fill L 0 Prove that

A: What is Antiderivative: In calculus, a differentiable function F whose derivative is identical to…

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: Prove that cos x cos y ≤ x - y for all x, y = R.

A: Mean value Theorem : Let a function  f:[a,b]→ℝ be such that    (i) f is continuous on [a,b] (ii) f…

Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

A:

Q: [S (x2 - Dx + 17) dx, = 7. (40.5) о The base b is: а) 20 b)22 с) 21 d) 23

A: First you have to know how to calculate base  Fisrt find D  then use the formula b = D * upper limit…

Q: FOo=X-1 de fined 2n E- lro] show that Fis Riemenn integruhk

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Q: Prove 2- = =4 has infinite many Solu thans ZEC.

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Q: de a+bcose' where a> bl. Hence or otherwise evaluate 2n de √√2-cose 3

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Q: Prove that Vtan a de – 7//2.

A:

Q: Prove the following identity: (x + y)2- (x-y)? = 4xy %3D

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Q: d tant lea) de tan' L) Itx? 2x THlege THe" ux 2) la 2x ln x Ids 2 lox t 2 y de 4(2/ax+2) 3) fL7)-6…

A:

Q: T/2 TT/6 sin x 2 1.)Prove that

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Q: ) Prove that sac"()/T sec

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Q: prove that f(x) = x sin√x is not [0,00) uniformly Continums

A: fx=xsinx We have to show fx is not uniformly continuous on [0,∞)

Q: Let A and u be positive real numbers. Then Jp(Ax) and Jp(ux) satisfy d d + dx dx (11.6.37) d ( d p²…

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Q: dr is divergent a true b) false

A: We have to calculate  ∫1∞1x2 dx.

Q: let 19, b) = 1, them prove that there exists x20 Such that ijzo ax_by = 1

A: