Let X=(1,0, – 1,-/2)'. Then, ||X||2 = Select one:

Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

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Q: Let Un−1(x) be defined for n ≥ 1and define U−1(x) = 0. Show that Tn(x) = Un(x) − xUn−1(x), for n ≥ 0

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Q: Find 1-a Conf int for y txo P( - tor;ou L T L tarziv) =1-a

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Q: If h(x) — За — — 1, j(x) k(x) = 21x? – 26x – 11 , show - 7x + 11 , and - - - - h(x) · j(x) = k(x).

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Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

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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: Prove that Jn (x) X good dx=1. n

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Q: 2 Find つえdy 2 こ( beny s)

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Q: 3,2 Evaluate the integral xx + x +2 dx%3D

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Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: 13. - (In t ² )º t dt

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Q: Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.19). L(x) =…

A: Here f(x)=lnx at x=1We have to find the linear approximation of f(x) andAlso find the value…

Q: If u= In x, then 1- (In x)2 dx=?

A: Find your answer below

Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: Differentiate the following with respect to x: b) 3*Inx

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Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: Suppose, X|0~ Binom(m.0)and e- Beta(a,B), then Var (Y) is equals to, maß

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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: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: Fincd dy for y-sinner} er tot

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

Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

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Q: (z In z + 5)dz

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Q: per integral test, (-1)" A) Σ B) none of these en (-1)" dz behaves like

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Q: Fn C) = show sin nx ス|L Sinnx

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Q: Put that: coshx- hel x+Jx=I/,.- cosh x= lml x+J xI/ メン」

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Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: ons z = sin y arn

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Q: If u In x, then 1-(In x)2 dx =?

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Q: y²

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Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

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

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

Q: 4. Prove 1 < | V1+ a dx <2 0,

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Q: 19. f(x. y) In(1 - x - y) %3D

A: As per our company guidelines we are supposed to answer only the first question that you have…

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

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Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

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Q: e){x*,x%,x}on(0,)

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Q: EA H.w : Does. fcz)= Continuous at cis

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Q: d'y on of x

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