1

If $a, b, x,$ and $y$ are all positive and $a+b=1,$ evaluate (a) $\lim _{p \rightarrow 0} \frac{\ln \left(a x^{p}+b y^{p}\right)}{p}$ (b) $\lim _{p \rightarrow 0}\l...

Question

If $a, b, x,$ and $y$ are all positive and $a+b=1,$ evaluate (a) $\lim _{p \rightarrow 0} \frac{\ln \left(a x^{p}+b y^{p}\right)}{p}$ (b) $\lim _{p \rightarrow 0}\left(a x^{p}+b y^{p}\right)^{1 / p}$

If $a, b, x,$ and $y$ are all positive and $a+b=1,$ evaluate (a) $\lim _{p \rightarrow 0} \frac{\ln \left(a x^{p}+b y^{p}\right)}{p}$ (b) $\lim _{p \rightarrow 0}\left(a x^{p}+b y^{p}\right)^{1 / p}$



Answers

(a) Evaluate $ \lim_{x \to ^x} x \sin \frac {1}{x}. $
(b) Evaluate $ \lim_{x \to 0} x \sin \frac{1}{x}. $
(c) Illustrate parts (a) and (b) by graphing $ y = x \sin (1/x). $


Similar Solved Questions

5 answers
Apoint source of light illuminates an aperture 2.00 m away: A 13.5 cm -wide bright patch of light appears on a screen 1.10 m behind the aperturePart AHow wide is the aperture? Express your answer with the appropriate units:pAValueUnitsSubmitRequest Answer
Apoint source of light illuminates an aperture 2.00 m away: A 13.5 cm -wide bright patch of light appears on a screen 1.10 m behind the aperture Part A How wide is the aperture? Express your answer with the appropriate units: pA Value Units Submit Request Answer...
5 answers
Find the characteristic polynomial ofthe following matrixA) (1 -a)(l + 390 - 6 - a) (B) (1 -a)(A + 3)0 - 6) (C) (1 -a)(l+3)0} - 6 - a) (D) A(1 + 3)0 - 6 - a) E) (1 - a)(l+3)02 - 6 - a) (F) A(1 + 3)01 - 15 - a) (G) (1 -a)(l+3)01 +6 - a) (H) A0 + 3)01 - 3 - a)
Find the characteristic polynomial ofthe following matrix A) (1 -a)(l + 390 - 6 - a) (B) (1 -a)(A + 3)0 - 6) (C) (1 -a)(l+3)0} - 6 - a) (D) A(1 + 3)0 - 6 - a) E) (1 - a)(l+3)02 - 6 - a) (F) A(1 + 3)01 - 15 - a) (G) (1 -a)(l+3)01 +6 - a) (H) A0 + 3)01 - 3 - a)...
5 answers
Point) Find the value of a for which~222is inithe setH #hspan5
point) Find the value of a for which ~2 22 is inithe set H #hspan 5...
5 answers
Skill Building Exercise: MO basis of nucleophiles and electrophiles/ Problem 6Show all of the electrophilic centers in the following compound: Fill numbers from left to right, from up to down.Click if you would like to Show Work for this question: Open Show Work
Skill Building Exercise: MO basis of nucleophiles and electrophiles/ Problem 6 Show all of the electrophilic centers in the following compound: Fill numbers from left to right, from up to down. Click if you would like to Show Work for this question: Open Show Work...
4 answers
Shirt business erpected enerale 545 0jj EToim abihn vean? 43,000 00J}e"EnuYeitreinvestedbusinessTate o/ 34:compounded conuinucusly nhidi Ede45lototal accumulated Yalu ol this Untente45 0n0 20 0145,0j0 00 %Wzete
shirt business erpected enerale 545 0jj EToim abihn vean? 43,000 00J} e"Enu Yeit reinvested business Tate o/ 34: compounded conuinucusly nhidi Ede45lo total accumulated Yalu ol this Untente 45 0n0 20 01 45,0j0 00 % Wzete...
5 answers
P(X)= 31X-0.3x2-250 for_02X4100 What_iS_the mrginal profit functon?
P(X)= 31X-0.3x2-250 for_02X4100 What_iS_the mrginal profit functon?...
5 answers
Reaction review. The preparation of the following compounds requires more than one step. As in Problem 41 , suggest a monosubstituted benzene as starting material and the reagents for all the steps needed to complete their synthesis.
Reaction review. The preparation of the following compounds requires more than one step. As in Problem 41 , suggest a monosubstituted benzene as starting material and the reagents for all the steps needed to complete their synthesis....
5 answers
The figure shows two wires carrying each a current of 3.0 mA What's the magnitude of the magnetic field at point 0,ata distance of 2mm from each wire?Select one:0.6 uT,out of the page b. 0.6 pT,into the pageZero
The figure shows two wires carrying each a current of 3.0 mA What's the magnitude of the magnetic field at point 0,ata distance of 2mm from each wire? Select one: 0.6 uT,out of the page b. 0.6 pT,into the page Zero...
5 answers
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$b b^{2} b^{3}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents. $$ b b^{2} b^{3} $$...
5 answers
The tires on a car have a radius of 31 cm.What is the angular speed of these tires when the car is drivenat 12 m/sm/s ?Express your answer using two significant figures.
The tires on a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 12 m/sm/s ? Express your answer using two significant figures....
5 answers
X5.4922 6.7388 2.5084 3.9084 3.901 4.7704 8.3117 7.7402 7.6467 9.050810 10 10 10 10
X 5.4922 6.7388 2.5084 3.9084 3.901 4.7704 8.3117 7.7402 7.6467 9.0508 10 10 10 10 10...
5 answers
Pontide ponc;presen;pepticNHjCHZCHzCHzCHzHJCCHzCHiCH;CHzCHJ
pontide ponc; presen; peptic NHj CHZ CHz CHz CHz HJC CHz CHi CH; CHz CHJ...
5 answers
Find the limit.lim Vg? + sin (T sec x) XI0A Vg? + 1 0 B. 0 0c: 9 0 D 1
Find the limit. lim Vg? + sin (T sec x) XI 0A Vg? + 1 0 B. 0 0c: 9 0 D 1...
5 answers
P24 pg/mi 10108.1010108.I/8100.I/N10108.1 108.1/t 108.1/010 *10?10101214 days after transtection2) Quantitative skills: Using the graph below; determine the approximate concentration of p24 capsid protein (in kg/L) after 6 days of transfection with the 168.1/R molecular clone:Include your calculations within the following space: The concentration of p24 capsid protein after 6 days of transfection with the 168.1/RJo J
P24 pg/mi 10 108.10 10 108.I/8 100.I/N 10 108.1 108.1/t 108.1/0 10 * 10? 10 10 12 14 days after transtection 2) Quantitative skills: Using the graph below; determine the approximate concentration of p24 capsid protein (in kg/L) after 6 days of transfection with the 168.1/R molecular clone: Include y...
5 answers
Question 46 ptsSolve the given differential equation by undetermined coefficients Please show all work and upload a file (PDF, JPG,DOCX) of the work and circle your final answer:3y" + 3y y = e +1Upload Choose a File
Question 4 6 pts Solve the given differential equation by undetermined coefficients Please show all work and upload a file (PDF, JPG,DOCX) of the work and circle your final answer: 3y" + 3y y = e +1 Upload Choose a File...
5 answers
Tata[} ~[J * [J EHH] -[HHS} ~G [} -[HE] Imetcheltha saote cellyi arethaspmnotR? } Dtou mnlchoona uucheeldles thecorrtrteaDananniWuut bttr biuie Lnc LAenlall7 oZmarer^- [: %ukm [ 3^ [C %"d[: 94' % ~[ :H [? % xl; % [ ;1 a [: % [ %Maeeenan~ena^- [ H-entoee-[ : % Huelne eulenornea tru Kne [email protected] AuEeeaahahcatarbeiUnnMneneereEeTnnenea
Tata [} ~[J * [J EHH] -[HHS} ~G [} -[HE] Imetcheltha saote cellyi arethaspmnotR? } Dtou mnlchoona uucheeldles thecorrtrtea Dananni Wuut bttr biuie Lnc LAenlall7 o Zmarer^- [: %ukm [ 3^ [C % "d[: 94' % ~[ :H [? % xl; % [ ;1 a [: % [ % Maeeenan ~ena^- [ H-entoee-[ : % Huelne eulenornea tru K...

-- 0.021452--