Q3) a) 42? Use Mean value theorem to show that for all a E (0, , 4 tan z 2

Q: 2. Show that by using MEAN VALUE THEOREM . u-v < tan-1 v - tanu < if 1+v2 u-v 1+p2 0< u<v and ded…

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Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

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Q: 15: Using first principles (by definition), prove thát thể đêrivätive of ä constant is U

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: Prove thiat dx Ś (areten()) ) = し 4+X

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Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

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

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Q: sent that by a positiv ntity N(0) is 2.

A: Given as, dNdt=?N0=?

Q: defined BCX,x). a norm Dn

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Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

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

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Q: y Verify Euler's theorem for u = x' In

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Q: When using Simpson's rule we must having two distinct point Select one: O True O False

A: Simpson's rule is used to calculate the value of definite integral by approximating area of the cure…

Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

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Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: (6) If u, =*-!P«(x)Pn -1(x) dx, show that nu, + (n – 1)n-1 = 2, %3D and hence evaluate u„.

A: Given un=∫-11x-1PnxPn-1xdx

Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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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: az Find if yz – In z = x + y ax

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Q: Let X and Y be independent and distributed as N(mu, 1). Is T=X-Y sufficient?

A: According to factorization theorem, if the likelihood function Lx,θ can be expressed in the form.…

Q: 5. Use the Mean Value Theorem to establish the following inequality |cos r- cos y < |r – yl, for 1,…

A: According to the guideline we should have been able to solve only first one question at a time

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Четверг show that the inu of a bounded E tix-oy ne 7 8. use T

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Q: 4. Let xn → 0 and (yn) be bounded. Prove xnYn → 0.

A: Hello, thanks for your question but according to our guidelines I am answering just question number…

Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

Q: (a, o) is not measurable. ylgn ihi

A: Given :-(a, ∞) is not measurable.

Q: 1. (10 + 7i )®

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Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

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

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Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

Q: 3. If f is continuous and | f(2) dr = 10, find | af(x*) dr. %3D Give proper reasoning.

A: It is given that if f is continuous and ∫09f(x)dx=10 We have to find ∫03xf(x2)dx=?

Q: Prove that S. 8 dx √π 2

A: This question is related to integration using gamma function.

Q: Use the Mean Value Theorem to prove that, for all x, y € IR, cos x - cos y ≤|x-y.

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Q: 4.* Let u be a harmonic function in R" and suppose that lu(x)/*dx < oo. R" Show that u = 0. (Hint:…

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Q: Pind using: 17 (a) Euler's Criterion (b) Gaur gn

A: We have given (517). we have to solve by using  a) Euler's criterion b) gauss lemma c) A primitive…

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the gi does not exist,…

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Q: Let f be in R[a, b]. Prove that -- f is in R[a, b] and ∫a b -- f(x)dx = -- ∫ab f(x)dx.

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Q: Prove that S, pm (x)Pn(x)dx = 0 if m# n ? %3D

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Q: 3)suppose fle) isadifferentialle fmehon on the intervall E-7,J Such that Hl-7) =4 and fl)=1.…

A: Intermediate value theorem

Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…