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# (20 points) Suppose that sequence of measurable functions fn Xx[0,&] is given such tat < fn+(z) < fn(r) for all _ eX Assume further that fi â‚¬ L'...

## Question

###### (20 points) Suppose that sequence of measurable functions fn Xx[0,&] is given such tat < fn+(z) < fn(r) for all _ eX Assume further that fi â‚¬ L'(X,e) i.e Jx f dp < &. Show thatlim +00J, dp Ks duHint: Use the convergence theorems! Bonus question (10 points): Show by counterex- ample that the conelusion is false if f 4 L'(Xp).

(20 points) Suppose that sequence of measurable functions fn Xx[0,&] is given such tat < fn+(z) < fn(r) for all _ eX Assume further that fi â‚¬ L'(X,e) i.e Jx f dp < &. Show that lim +00 J, dp Ks du Hint: Use the convergence theorems! Bonus question (10 points): Show by counterex- ample that the conelusion is false if f 4 L'(Xp).  #### Similar Solved Questions

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hQZH 9h #0 7ubXawQu) Kyavdl Auan "JUQQJAOLUI u0nj?p? MOYS 01 SMOLE pJAIn? Jsn pue 'so81ey? pue SQICIPJULJIUI Ile ?pnpou] "JOJ Pinoj pnpoId S4 MOY ue[dxa 01 WSIUBYDJU osodoxd "UOLJBJI SIYI UL QLLJOJ PInOJ JEY} spnpOJd ajqissod Inoj Jq1 JO JUO SEM juexoyopKoau?[AQOW...
##### Students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. The table below shows the resuks there difference the mean hours slept on wee knights versus weekends? Use significance level of & 0.05S-udentWeeknight Hours Weekend Hours10.5paired t-test requires that the samples be dependent: that condition met for this problem? Why or why no: (2 point)State the hypotheses symbols_ (2 points)Use your = culator to perform t-test on L3 - L1 -LZ
Students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. The table below shows the resuks there difference the mean hours slept on wee knights versus weekends? Use significance level of & 0.05 S-udent Weeknight Hours Weekend Hours 10.5 pai...
##### Vector (6,8 8 direction in the1 at tne4 [ directional derivative of the exact answer using radicals as needed ) derivative is Compute directiona The (Type
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##### 8 Solve 251-3 = 51_
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##### The peak 2.75 ppm 0 repi esents p alWhat . Wha element What kind elementisthe What kind ot hond does H Is the CHZ represented by bend belwpenke 5 bondbelpenke thc unsaluration CHrepresented by thelHNMR peak at HNMR [7 (eteanznsm represent? A therc In the molecule? peak at 3.95 ppM represent? A (single; functional group 3,40 ppm DUE 'aiauis) bonded to? bondedto? double. double triple) triple)
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##### Exercise !, Question ! (drag the correct answer to the box) a) the sample size (n) for each site is 30 b) the site that contains the largest fish is Antigonishc) the site that contains the smallest fish is GuysboroughPort Hawkesbury
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##### Jx(: = ")y(v) du. (Hint: Try the sulstitutionShow thnt dp < 4 = =I+ V,v =v)
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##### Problem 3 A 10" x 10" x 10" cube has 10" diameter holes drilled perpendicularly through the centers of each face. Use hit and miss integration to estimate the remaining volume. Column headings for a possible implementation in excel are given below.Random Random Random Outside Outside cylinder 12 cylinder 22Outside cylinder 32Within remaining volume
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##### 20. [0/2 Points]DETAILSPREVIOUS ANSWERSSCALCET9 4.XP.1.027.MI:Find the absolute minimum and absolute maximum values of f on the given interval_f(t)tv 9[-1, 3]absolute minimum value2absolute maximum value2V 2Need Help?Read ItWatch ItMaster It21. [0/2 Points]DETAILSPREVIOUS ANSWERSSCALCET9 4.1.061.MI:Find the absolute minimum and absolute maximum values of f on the given interval_f(t) 12 cos(t) + 6 sin(2t) ,2absolute minimum value9v3absolute maximum valueNeed Help?Rcad ItWatch ItMaster It
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##### Fralluu 7. ln I701_ Issac Newton praved his Law o Cooling:; Tlt) = Ae"t+Ta, "bich ia aut exponential model that relates the temperature of an object T a function of cut (ue will us2 minutes) that is placed in euvirontnent with atnbient temperatureSuppose cup of hot coflce seritd at 180'F and placed in romn with ambient temperature 68" _ After minute, the cup of coffce has temperature of 147PF:Create model using the Newton" Law of Cooling template:(b) What will be the tem
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##### 0.00210 M solution of a substance with a molar What is the transmittance of a absorptivity of 313 M Icm ! ina cell with a 1.00 cm path length:0.2201.520.0310.657
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##### Sketch the graph of an example of a function $f$ that satisfies all of the given conditions. $\displaystyle \lim_{x \to 0^-}f(x) = -1$, $\displaystyle \lim_{x \to 0^+}f(x) = 2$, $f(0) = 1$
Sketch the graph of an example of a function $f$ that satisfies all of the given conditions. $\displaystyle \lim_{x \to 0^-}f(x) = -1$, $\displaystyle \lim_{x \to 0^+}f(x) = 2$, $f(0) = 1$...