2. TER-1 to be, Hn E IN 1+r+4---+ 1-r Shoh that

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: then 7(1 - а)М? + 6(1 - а) Мт %3D ВM?, 7(1 - а)т? + 6(1 — а)Мт %3D Вт?, Subtracting we obtain Y(1 –…

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Q: E. Prove the following: 四- Iz.l 1.

A:

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

A:

Q: If I, = S e cos" xdx, where n > 2, prove that In 1+n(n-1)In-2 n² +1

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Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: If A= then A" + nl is equal to 1.

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Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 2etūsw ER' such that and iov-2.Than (3ü)(B)

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Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: 9. Prove L'S 25+1 Cs+2)?(S-1)2. %3D

A: Consider F(s) = 2s+1(s+2)2(s-1)2                            (1) Let 2s+1(s+2)2(s-1)2 =…

Q: 27. Verify ldt ip|1| =x|x]. Hint: Consider x > 0 and x <0 separately.

A:

Q: A. Homo ge neous Higher Ordered DE (0-704 - 310° ° + 103o² 1030² + 1500 - 216) y:0

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Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

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Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

A:

Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: 3 E in (1 -) -in2 , . =-In2 =1 k2 –1 k=2

A: We will  use the limit of partial sum

Q: Show that (hcs) de = 1 In 27 e %3D 2. 20 (ite")(2 + 1)

A: To show: ∫0ln 2e2x1+ex2ex+1dx=12ln2720. Concept used: Integration of ∫1vdv is equal to ln v+C.…

Q: Q.2) Evaluate cln 7 cln 2 cln 5 e(z+y+3) dzdydr In 6 In 4

A: Given triple integral is ∫ln6 ln7∫0ln2∫ln4ln5 ex+y+z dz dy dx   Note:- ex+y+z =ex ey ez

Q: 1 -dr. a In r| Find 3.

A: Let's find.

Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

A:

Q: Prove inf { ñt nEN}= %3D

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: a n eln t--+

A: Given a function : h(x)=31-2x+2 We need to find the graph of this function.

Q: -2x -dx - Evaluate (1-x)' 8 А. х* + 6х- In(1-х)' + 1-х 8 -(1-x)* +C С. х? +6х+ In(1-х)' +- -(1–x)*…

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Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

Q: 13. - (In t ² )º t dt

A:

Q: If ADEF ARST, then we can conclude that ZR

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

Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

A: Seriese expansion

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: If E (ar + br) 2n and n+1 k=1 Σ (ακ-bk) -- 1, then Σa- n+2 k=1 k-1 O 2 3 2 O 1 5. 2 Ο None

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Q: it is unbaised estimated of a Then Show That ta is baised estimated of O2.

A:

Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

A:

Q: 9 Find A and A by Hamilt on Hheoren For A=|° E12s -75 -IS

A:

Q: 24. Find the Fowrier r fas - -IN X

A: Hv

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

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Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

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Q: If the mth term of an AP be 1/n .And nth term be 1/m.then show that it's (mn)th term is 1

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Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

Q: 12) a-:]- B-[:: ind AR 3 0 3 -2 1 Find AB. %3D -2 1 0 4-3

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Q: 9 show Itat Ihe maclayvin Sevies For Hense is メ+ メ t.. 4- X

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Q: Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn…

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: 1- In x)² If u=In x, then dx=? L'a-wdu A B

A: From the given integral: I=∫ee21-lnx2xdx   ...1

Q: By 2 Cas X the Same. way prove that

A: Prove that J-12x=2πx cosx

Q: 14. If u(x, y) = x² cosh(xy² + 1), evaluate in the simplest term the expression ди 2х ди -- ax

A: We are using partial differentiation techniques. we have to recall the formula for differentiation…

Q: what expressi on is equivaient to this. (n-a)!

A: n!(n-2)!+n=n×(n-1)×(n-2)!(n-2)!+n  [we use the idea of factorial]=n(n-1)+n=n2-n+n  [distribute n]=n2

Q: Write equation for each ellipse

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.