Loading [MathJax]/jax/element/mml/optable/GeneralPunctuation.js
 

heureka

avatar
Benutzernameheureka
Punkte26396
Membership
Stats
Fragen 17
Antworten 5678

 #2
avatar+26396 
+34

a/(a+b)+a*a/(a*a-b*b)+b/(a-b)=?

 

aa+b+a(aaabb)+bab=aa+b+aaaabb+bab=aa+b+a2a2b2+bab|3. Binom  a2b2=(a+b)(ab)=aa+b+a2(a+b)(ab)+bab=aa+b+aa+baab+bab=aa+b(1+aab)+bab=aa+b(ab+aab)+bab=aa+b(2abab)+bab=1ab(a(2ab)a+b+b)=1ab(a(2ab)+b(a+b)a+b)=a(2ab)+b(a+b)(ab)(a+b)=2a2ab+ba+b2(ab)(a+b)|ab+ba=0=2a2+b2(ab)(a+b)|3. Binom  (a+b)(ab)=a2b2=2a2+b2a2b2aa+b+a(aaabb)+bab=2a2+b2a2b2

laugh

.
22.10.2015
 #4
avatar+26396 
+30

 

Part 2:

 

limx0(sin(x)x)cot(x)= ?(sin(x)x)cot(x)=eln(sin(x)x)cot(x)=eln(1+sin(x)xx)cot(x)ln(1+sin(x)xx)cot(x)=[(x23!+x45!x67!+x89!+)112(x23!+x45!x67!+x89!+)2+13(x23!+x45!x67!+x89!+)314(x23!+x45!x67!+x89!+)4](1x13x145x32945x514725x7)

 

ln(1+sin(x)xx)cot(x)=[(x26+x4120x65040+x840320+)12(x436x6360+41x8302400+)+13(x6216+x81440+)14(x81296+)](1x13x145x32945x514725x7)

 

 

until x7:

 

ln(1+sin(x)xx)cot(x)=×(1x):x6+x3120x55040+x740320+x372+x572041x7604800+x5648+x74320+x75184+×(1x3):+x318x5360+x715120++x5216x72160++x71944+×(1x345):+x5270x75400++x73240+×(2x5945):+x72835+

 

ln(1+sin(x)xx)cot(x)=x6+x3(1120172+118)+x5(15040+172016481360+1216+1270)+x7(14032041604800+1432015184+11512012160+1194415400+13240+12835)+ ln(1+sin(x)xx)cot(x)=x6+x320+59x511340+401x7680400+ limx0(sin(x)x)cot(x)=limx0eln(sin(x)x)cot(x)=limx0eln(1+sin(x)xx)cot(x)=limx0ex6+x320+59x511340+401x7680400+=e0 limx0(sin(x)x)cot(x)=1 

 

ready.

 

laugh

21.10.2015
 #3
avatar+26396 
+30

limx0(sin(x)x)cot(x)= ?

 

Part 1:

We need

 

 cot(x)=1x13x145x32945x514725x7ln(1+x)=xx22+x33x44+sin(x)=xx33!+x55!x77!+x99!+sin(x)x=x33!+x55!x77!+x99!+sin(x)xx=x23!+x45!x67!+x89!+sin(x)x=1+(sin(x)x1)=1+sin(x)xx 

 

 ln(1+z)=zz22+z33z44+z=sin(x)xx=x23!+x45!x67!+x89!+ln(1+sin(x)xx)=(x23!+x45!x67!+x89!+)112(x23!+x45!x67!+x89!+)2+13(x23!+x45!x67!+x89!+)314(x23!+x45!x67!+x89!+)4 

continued...

 

laugh

21.10.2015