& B= Q1-Let A = 2 4 Verify that (AB)" = B" A"

Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: sn'x プェ Sec'x-1 from [o, of 2.

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Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: The DE : y'= e 5x-7y is seperable Select one: O True False

A: We have cheek

Q: The DE : y' = e>x-7V is seperable Select one: O True O False

A: Try to separate the variables if it is possible than given DE is separable.

Q: & b. su j+ byz²

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Q: 1. S ef = c f

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Q: Show that x +2 and oe) = *+6

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Q: Solve for z if cosh z = V3i.

A: Simply put cosh z= 1/2(e^z+e^-z)  Then simplify  then finally got quadratic in e^z  then find the…

Q: Use two different methods to calculate dzu/ar if u = /x² + y². = est, and y = 1 + s² cosz. IUse two…

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Q: f(1) = 3e " cosh (In 2r) -21

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Q: Show Sn+3 diverges by osing 6n +5 the test for divegence 1こV

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Q: Let Xn ☆ Bil^,p] where n& P ae wnknown. Find method of moments estimators for n&

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: 7) In AXYZ, mLY 80, XY = 14, and XZ 17. To the nearest tenth, what is mLZ? %3D

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Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: 2.5 Solve for z if cosh z = V3i.

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Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

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: 3. From Eq. (1), deduce that U2n-1 2. U2n 2. %D %3D n 2

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: cancer u alcurate 5th on diagnostic test is 9s 2 those who halse A 'cancer cnd on those wno do not

A: Given that, As the test is 95% accurate for both who have cancer and who don’t, therefore the…

Q: Find solution n f(x) 300 2.4771 x (301) using newton backward 304 2.4829 305 2.4843 interpolation…

A: Introduction: Interpolating polynomial is the polynomial having the least possible degree that…

Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: The DE : y' =e3x-7Y is seperable Select one: O True False

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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: (14) Approximate S, x² ex², Using Simpson's rule dp,

A: Simpson's rule is a numerical method used to approximate the definite integral which represents the…

Q: Solve for z if cosh z = v3i.

A: Given cosh z=3ι. Expand cosh z to solve for z.             ez+e-z2=3ι              ez+e-z=23ι…

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: az given that yz*+x2z3 = eyz ax

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Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

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Q: Ques tion 1 : that Given 2 x?y" + x y' + 3y= 0 show 2x* ylara) lanni)x ylurs) + (2n2.n +3) ym)-

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Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

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Q: 4 In GL(2,Z13), det 1 4

A: We have to find the determinant using GL(2,Z13) That is, instead of usual addition and…

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

Q: Find the antiderivative of: dt/(1-7t)^3 where  u = 1-7t

A: To find antiderivative

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: N 25 )X= 125 SX2 = 650 EY2 = 460 EXY = 508 t was, however, later on discovered at the time of…

A: Given: N=25 ∑X = 125, ∑Y= 100 ∑X2=650 ∑Y2=460 ∑XY=508 Two pairs are taken as (6, 14) and (8,6)…

Q: et. 4=-4 and V=S, let 7x) = 4x42C4S 7x) Lnd the wolve of cE (u,v) such that 7'cc)=qc4)-7CV value…

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Q: Find dr. J (1+z²)3/2 - In Vx² + 1 + x| + In |Vx² + 1 + x| - Ja? + 1 +c Vx² + 1 O Option 3 Option 1…

A: Let I= ∫x21+x232dx Let x=tanθ ⇒dx = sec2θdθ Substituting this in I, we get

Q: A) Vn +5 B) is larger than Vn + 5 1.

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Q: = 11% and E = 715, calculate the Еxample 4: If К. stock value of XYZ Ltd. for: 2) r= 11%

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Q: ds if s = dt t Find 7t +2

A: S=t7t+2 We need to find dSdt