Question
7 . Suppose f is continuous on D and holomorphic on D- (a Show that |fl attains its maximum 0n the boundary €D. That iS, show that there is w € €D such that |f(2)l < |f (w)l for every 2 € D. (Hint: The assertion is clear if f is constant_ Assume f is not constant Since |f | is continuous on D which is a closed and bounded set) , by the extreme value theorem, |fl has a maximum 0n D. Can this maximum be in D? See the maximum modulus principle (Theorem 4.5, page 92 of Stein-Shakarchi).)
7 . Suppose f is continuous on D and holomorphic on D- (a Show that |fl attains its maximum 0n the boundary €D. That iS, show that there is w € €D such that |f(2)l < |f (w)l for every 2 € D. (Hint: The assertion is clear if f is constant_ Assume f is not constant Since |f | is continuous on D which is a closed and bounded set) , by the extreme value theorem, |fl has a maximum 0n D. Can this maximum be in D? See the maximum modulus principle (Theorem 4.5, page 92 of Stein-Shakarchi).)
Answers
Suppose $f$ is a continuous odd function such that $f(a)$ is a relative maximum. What can be said about $f(-a) ?$
Similar Solved Questions
5 answers
(20 pts total) (25.5) Ten samples of size wore taken Irom production Iot of bolts Tro ' values (length mm) are as snown Assuming the populalion was normal with mean of 27.5 and variance 0.024, set UP conlng chart for tne mean and put (he sample means the chart:Sample # 10 Sample 27.4 27.4 27.5 27.3 27.9 27.6 27.6 27.8 27.5 27.3 Values 27.6 27.4 27.7 27.4 27.5 27.5 27.4 27.3 27.4 27.7
(20 pts total) (25.5) Ten samples of size wore taken Irom production Iot of bolts Tro ' values (length mm) are as snown Assuming the populalion was normal with mean of 27.5 and variance 0.024, set UP conlng chart for tne mean and put (he sample means the chart: Sample # 10 Sample 27.4 27.4 27.5...
5 answers
#pani RemanCalcr7 5 0 0u5-MIS0. Find tne cost functon:cbeolute values where apErcpnatu fcommany % marginu costtunctnaMc(x)cur)Need Help?Submeruaa3444 ProgrubaPncbce Anolher Yufalon
#pani RemanCalcr7 5 0 0u5-MI S0. Find tne cost functon: cbeolute values where apErcpnatu f commany % marginu costtunctna Mc(x) cur) Need Help? Submeruaa 3444 Progruba Pncbce Anolher Yufalon...
2 answers
5 . Identily the lettered inlermediales in the following reaction sequence: Whenmixtureortho and para producis resultselectrophilic aromatic substitution,consider the para product only-CH;COCIFeBrsAICI,I[t] CH;CHO Ju2]H,o PCCShow melhod I0 carry oul Ihe lollowing transiormation using Grignard reagent: Which roule:CHOWhich of the following carboxylic acid has Ihe lowest pka?COOHCOOHCOOHCOOHCOOHH;CoOzN8. Amino acids exist as zwitlerion, they are too polar t0 be soluble in organic solvents Iike
5 . Identily the lettered inlermediales in the following reaction sequence: When mixture ortho and para producis results electrophilic aromatic substitution, consider the para product only- CH;COCI FeBrs AICI, I[t] CH;CHO Ju2]H,o PCC Show melhod I0 carry oul Ihe lollowing transiormation using Gr...
4 answers
Positive 0i neblnve crpiai:The Harvard College Alcohol Study fnds that 67% of college students support efforts to "crack down on underage drinking Does this result hold at a large local college To find out, college administrators survey a SRS of 100 students and Itind that 62 support a crackdown on underage drinking a) Suppose that the proportion ofall students attending this college who support a crackdown is 67%, the same as the natonal proportion. What is the probability that the proport
positive 0i neblnve crpiai: The Harvard College Alcohol Study fnds that 67% of college students support efforts to "crack down on underage drinking Does this result hold at a large local college To find out, college administrators survey a SRS of 100 students and Itind that 62 support a crackdo...
5 answers
Write an equation for the quadratic x-intercepts: graphed (1,0) below: and (3,0); y-intercept: (0,1)
Write an equation for the quadratic x-intercepts: graphed (1,0) below: and (3,0); y-intercept: (0,1)...
5 answers
Olptrutatagc family households tuth (hildrtn cungu Inun mton 19.4 Standard 4thotion: 5.3 (lfrom Lountics #t _ tuntry)About Wnat pucentagc 0F tounhts navt eldnn14134-7Of tntir naccholdsAbout What rurcentagclounhes nawt lulannIcss tnan I7. OF #ntir housc holds?
Olptrutatagc family households tuth (hildrtn cungu Inun mton 19.4 Standard 4thotion: 5.3 (lfrom Lountics #t _ tuntry) About Wnat pucentagc 0F tounhts navt eldnn 141 34-7 Of tntir naccholds About What rurcentagc lounhes nawt lulann Icss tnan I7. OF #ntir housc holds?...
5 answers
Queslion 9If the sample means for each of k treatment groups were identical (yes, this is extremely unlikely) , what would be the observed value of the ANOVA test statistic?Nol yet aanaweredMarked out ot 1001 Fleg queblionSelect one 0.,0A value between 0.0 and 1.0c.1.0d. A negative value
Queslion 9 If the sample means for each of k treatment groups were identical (yes, this is extremely unlikely) , what would be the observed value of the ANOVA test statistic? Nol yet aanawered Marked out ot 1001 Fleg queblion Select one 0.,0 A value between 0.0 and 1.0 c.1.0 d. A negative value...
5 answers
In the figure below, Rz 104 @ R2 = R3 53.5 0. R4 75.0 02, and the Ideal battery has emf 8 = 6.00 V:What Is the equivalent resistance?(b) What is / In R1?(C) What Is / in Rz?(d) What Is / In R3?(C) What Is / in R4?
In the figure below, Rz 104 @ R2 = R3 53.5 0. R4 75.0 02, and the Ideal battery has emf 8 = 6.00 V: What Is the equivalent resistance? (b) What is / In R1? (C) What Is / in Rz? (d) What Is / In R3? (C) What Is / in R4?...
5 answers
Question 3.5-7. Nitrogen [8 marks] In the nitrogen cyclc, there are three types of nitrogen fixation (a) Balance the following half equations depicting bacterial fixation (nitrogenase) and denitrilicalivn: (2 marks)Nslg) NH: (aq) +Hxg) NO; (44) Nlg)(b) In process culled nitrilicution_ enzyinE cutalyse the conversiun auonAM (NIL' ) Io nitrate (NO; ) using oxygen the oxidant. Provide balanced chcmical equation for the overall process. Show Fowr wok marks}NH (d4) - NOx (aq) 0-(aq) H-Ol)Determi
Question 3.5-7. Nitrogen [8 marks] In the nitrogen cyclc, there are three types of nitrogen fixation (a) Balance the following half equations depicting bacterial fixation (nitrogenase) and denitrilicalivn: (2 marks) Nslg) NH: (aq) +Hxg) NO; (44) Nlg) (b) In process culled nitrilicution_ enzyinE cuta...
5 answers
For problems that ask for the use of mathematical softwares, include both copies of the plots and copies of the codes, even if the codes were adapted from codes in the book: Collaboration and discussion are encouraged, but do not copy solutions.
For problems that ask for the use of mathematical softwares, include both copies of the plots and copies of the codes, even if the codes were adapted from codes in the book: Collaboration and discussion are encouraged, but do not copy solutions....
5 answers
Sin % = sinx coshy + i cos x sinh ysin1 C0sz2 F cosz1 sinzz = sin(z1 ~ Z2)Cosz1 C0szz + sinz1 sinzz = cos(z1 + Z2)CoSz1 C0SZz I sinz1 sinzz = cos(z1 L 22cos z = CoS zsin(-z) = _ sin %cos(-z) = Cos ztan(-z) =-tanzcot(-z) = cot z
sin % = sinx coshy + i cos x sinh y sin1 C0sz2 F cosz1 sinzz = sin(z1 ~ Z2) Cosz1 C0szz + sinz1 sinzz = cos(z1 + Z2) CoSz1 C0SZz I sinz1 sinzz = cos(z1 L 22 cos z = CoS z sin(-z) = _ sin % cos(-z) = Cos z tan(-z) =-tanz cot(-z) = cot z...
5 answers
Add or subtract as indicated.$$8+ rac{3}{x}$$
Add or subtract as indicated. $$8+\frac{3}{x}$$...
5 answers
PLEASE HELP 2. The simulation takes you through a bomb calorimeter, wherethe volume of the reaction chambre is constant and it tells youthat the equation you are using is ΔH = C∙ΔT, where C is theoverall heat capacity and ΔT is the change in temperature. Theythen later go on to calculate ΔU, the change in internal energy,using the equation ΔH = ΔU + Δ(pV), which they approximated to beequal to ΔH because the Δ(pV) term was so small. In this case, ΔHand ΔU are very close to each othe
PLEASE HELP 2. The simulation takes you through a bomb calorimeter, where the volume of the reaction chambre is constant and it tells you that the equation you are using is ΔH = C∙ΔT, where C is the overall heat capacity and ΔT is the change in temperature. They then later go on t...
5 answers
EnaaFnalnnaa Ctkhtalfolowtng subtttuent % 121 Lecne #ctnct tie meta darctotproduct(s) the follotng rcachons maio13} PredictKn-On2-(+a) Hci^4AIclsSc; RiSc _AICI;
enaa Fnalnnaa Ctkhtal folowtng subtttuent % 121 Lecne #ctnct tie meta darctot product(s) the follotng rcachons maio 13} Predict Kn-On 2-(+a) Hci ^4 AIcls Sc; RiSc _ AICI;...
5 answers
Eleaso_helpme wll Queshon) aw showv sllk_skys; Prepose 0 Synthess of the fellowng_malewly ck3ouICc of_carba ad teluene qf only Wse ASePreQhelCh;
eleaso_helpme wll Queshon) aw showv sllk_skys; Prepose 0 Synthess of the fellowng_malewly ck3 ouICc of_carba ad teluene qf only Wse ASePreQhel Ch;...
5 answers
10.-/4 pointsLog(x) , f(x) g(x) , and f(x)g(x) Find f(x) + g(x) , f{x) fx) = x2 i1x + 18 g(x) = x + 2 +g(x)fx) g(X)f(x)g(x)Need Help?Rcxd [email protected] Mel
10. -/4 points Lo g(x) , f(x) g(x) , and f(x)g(x) Find f(x) + g(x) , f{x) fx) = x2 i1x + 18 g(x) = x + 2 +g(x) fx) g(X) f(x)g(x) Need Help? Rcxd W @hboa Mel...
2 answers
Verlfy that _LunsDaramerer famiysolutionsthe dlfferentlal equatlon y'Differentiating Differentiatingtan(* c) we get tan(* c) we getsec(* ory' = 1 + y2 sec (* c) or y' = 1 +Y2. tan(* c) we get v' tan?(x - c) ory' = 1 + v2 tan(* c) we get tan?(x c) ory" = 1 +y2, tan( * csc(x c) or y' - 1 + Y2.DlfferentiatingDifferentiatingDifferentiatingSince f(x, y) = 1 + y2 and dfidy 27 are continuous everywnere the region the first-order Initlal-value problem 1 +Y2 _ Y(0)Theo
Verlfy that _ Luns Daramerer famiy solutions the dlfferentlal equatlon y' Differentiating Differentiating tan(* c) we get tan(* c) we get sec(* ory' = 1 + y2 sec (* c) or y' = 1 +Y2. tan(* c) we get v' tan?(x - c) ory' = 1 + v2 tan(* c) we get tan?(x c) ory" = 1 +y2, t...
5 answers
Write down the mlcro-Instructions (T1 to T6) necessary to implement STA instruction SAP-1.STA x: where x is memory locationSTA copies the contents of Accumulator to the specified memory location [inverse of what LDA does] What changes are necessary in hardware/CON words for each T-state, to implement this instructionStateCON Word in BinaryCON Word Hex
Write down the mlcro-Instructions (T1 to T6) necessary to implement STA instruction SAP-1. STA x: where x is memory location STA copies the contents of Accumulator to the specified memory location [inverse of what LDA does] What changes are necessary in hardware/CON words for each T-state, to implem...
4 answers
Topic 3: Student study times (20 marks)A class survey in a large class for first-year college students asked, About how many hours do you study during typical week? The mean response of the 463 students was x = 13. hours. Suppose thal we know that the study time follows Normal distribution with standard deviation 0 = 7.4 hours in the population of all first-year students at this university.3a) Use the survey result to give 99% confidence interval for the mean study time of all first-year student
Topic 3: Student study times (20 marks) A class survey in a large class for first-year college students asked, About how many hours do you study during typical week? The mean response of the 463 students was x = 13. hours. Suppose thal we know that the study time follows Normal distribution with sta...