44. Rewrite each of the following as an equivalent expres- sion with a rational exponent. [R.5] а) b) VF 1 c) Vm d) Vx - 9

Q: Q3 Prove that In Coth x 1

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Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

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Q: If f is Caib], ab solute maxinum continouus on then f attains valye fcc) and an ab solute mirinum an…

A: Que: Ans : Given         f(x) is any continews function on [a, b]          Let f(c)  be absolute…

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: 3. 2 What is the value of the integral 7xyz dxdydz ? 0, Select one: O 133/4 O 135/4 O 137/4 O 139/4…

A: To evaluate: ∫23∫12∫017xyz2dxdydz Let I = ∫23∫12∫017xyz2dxdydz First integrate with respect to x and…

Q: Express In V16 in terms of In 2 and/or In In 16 =[ (Type an exact answer.)

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Q: Evaluate the followingintegrals.

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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: 2- Show that: (-1)m (2m + 1)! NIE

A: Solution:     Definition of Bessel's function:

Q: figure th

A: 1) Here we have to find the ∠RST=?

Q: Which of the following is NOT true about the DE: 6xr?ydx+2x³dy=0?

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Q: 22. Differentiate the following with respect to the variable x, giving your answer in a implified…

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Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

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Q: Consider the following. (If an answer does not exist, enter DNE. f(x) = In(x² + 7) %3D (Entor voUr

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Q: Suppose s(t) = 3t+ 6 on the interval [1, 4]. What is the displacement on [1, 4]? 06 08 09 O 18

A: topic-displacement

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

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Q: у" + Зу" + Зу' +у%3D0

A: We have to solve the differential equations

Q: So 3 Vit7x dx U-substiutson.

A: Use u substitutions to integration

Q: 2. Estimate the value of V22. + • V22 is between and but closer to Decimal estimate: 22-

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Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

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Q: Given: LM NO; ZLMO = ZNOM Prove: LO NM

A: Using Side angle side test,

Q: By using Residue fined S 2+3 sin z(z-1)² dz, C:|2|=2? (6 €13) (4

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Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: . Given: LM NO; ZLMO= LNOM Prove: LO NM Reasons

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Q: s. To our surprise, 38 of the s o select the response which co cription, which term best descri

A: prospective study : In this kind of study, subjects are studied by researchers before they develop…

Q: Compute the values (d,x,y) that the call Extended-Euclid(19177,26797) returns.

A: Find the extended euclid19177,26797.

Q: In ALMN, LN is extended through point N to point O, m/NLM = (x – 4)°, mZMNO = (4x – 17)°, and m/LMN…

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Q: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

A: Given, 2x²=1+5y² Here 5y2 is a multiple of 5 ending in digit 5 or 0. 2x2 can end in 1 or 6 But no…

Q: Show that yn ez, if n³+5 is odd then n is even For the toolbar, press ALT+F10 (PC) or ALT+FN+F10…

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Q: 5x 60(x, +x,) 3 b) Y = In 60(x2 . 3,

A: The given differential equation:                                                 Y=ln5x1360(x2+x1)32…

Q: Considere la ecuación diferencial dy/dx=−ax/y, con y(0)=11, determine el valor de a de modo que…

A: See the attachment

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: 3) Prove There exists a real nubrsSo Surh thot

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Q: In ALMN, LN is extended through point N to point 0, mZMNO = (5x – 13)°- mZNLM = (x – 4)°, and m/LMN…

A: Solution-

Q: Evaluate tne below exprassion using De Moivres meorem-

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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: Oprove Heed A A lnda = 2 - - where feass integmle even funchen

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Q: Find the lenegth of the cunde 312 2 from x=o to -

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Q: Show that, by det by b2 92 •92 =TT (ai-bi) br b2 b3 an

A: We have to show that det111⋯1b1a1a1⋯a1b1b2a2a2⋮⋮⋮⋮b1b2b3⋯an=∏i=1nai−bi Let us consider the matrix…

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

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

A: Prove that J-12x=2πx cosx

Q: (35 Show that the following grephes are Hameltonian 8) e a) d c) a ol

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Q: 19 When approximating | f(x) dr with 10 rectangles, what is Ar? O 1.8 O 19 O 10 O 1.9 18

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Q: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

Q: V. En el siguiente ejercicio obtenga la derivada de la función brindada. 5, y = In (2e¹ sen 1)

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Q: How do I subsitute X= Ztan into Ha):" ) How do I simphtiy asuming Ok Be

A: Solution : We have given a function fx = x4 + x2   To find : Substitute x = 2 tanθ into the given…