Calculus % 10. Series Prof. Schumann

Calculus - 10. Series Prof. Schumann
hand in: Jan 5, 2006
1. Determine the following limits
a)
ex + e x 2
lim
x!0
1 cos x
b)
1
lim x ln(1 + )
x!+1
x
c)
lim f(ln x) ln(1
x!1 0
x)g
d)
x3 + x2
x!1
x2
lim
x
1
1
2. Suppose that f 2 C 2 near x0 . Determine
lim
f (x0 + h)
h!0
2f (x0 ) + f (x0
h2
3.(* and voluntary) Determine the following limit
lim
x!+0
sin x
x
4. Read this poem:
Merry Christmas!!!
When the snow falls wunderbar
And the children happy are,
When the Glatteis on the street,
And we all a Gluehwein need,
Then you know, es ist soweit:
She is here, the Weihnachtszeit.
Every Parkhaus is besetzt,
Weil die people fahren jetzt
All to Kaufhof, Mediamarkt,
Kriegen nearly Herzinfarkt.
Shopping hirnverbrannte things
And the Christmasglocke rings.
1
1
x2
h)
Merry Christmas, merry Christmas,
Hear the music, see the lights,
Frohe Weihnacht, Frohe Weihnacht,
Merry Christmas allerseits ...
Mother in the kitchen bakes
Schoko-, Nuss- and Mandelkeks
Daddy in the Nebenraum
Schmücks a Riesen-Weihnachtsbaum
He is hanging auf the balls,
Then he from the Leiter falls ...
Finally the Kinderlein
To the Zimmer kommen rein
And es sings the family
Schauerlich: "Oh, Chistmastree!"
And then jeder in the house
Is packing die Geschenke aus.
Merry Christmas, merry Christmas,
Hear the music, see the lights,
Frohe Weihnacht, Frohe Weihnacht,
Merry Christmas allerseits ...
Mama …nds unter the Tanne
Eine brandnew Te‡on-Pfanne,
Papa gets a Schlips and Socken,
Everybody does frohlocken.
President speaks in TiVi,
All around is Harmonie.
Bis mother in the kitchen runs:
Im Ofen burns the Weihnachtsgans.
And so comes die Feuerwehr
With Tatü, tata daher,
And they bring a long, long Schlauch
And a long, long Leiter auch.
And they cry - "Wasser marsch!",
Christmas das is now im A... (Eimer)
Merry Christmas, merry Christmas,
Hear the music, see the lights,
Frohe Weihnacht, Frohe Weihnacht,
Merry Christmas allerseits...
——————————————————————————–
Christkindl‘s Weihnachtsseiten (http://www.weihnachtsseiten.de)
copyright c by Josef Dirschl, www.feiertagsseiten.de - [email protected]
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ALLE RECHTE VORBEHALTEN / ALL RIGHTS RESERVED
(and I thing c by Udo Jürgens)
Perhaps the German students can help their foreign fellow students.
5. Listen to the song of Udo Jürgens from exercise 3. (I can’t put the
song on the internet side, weil I sonst vielleicht ins prison muss and you keine
Vorlesung in calculus mehr have. What Jammer it would be.)
(By the way, I hope that my English in the lecture is somewhat better -:)
6.* Celebrate Christmas. Since you are an international group of students
some of you probably do not celebrate Christmas. Then go to exercise 7.
7. Take my best wishes for a good, successful and healthy year 2006.
Sincerely
Rainer Schumann
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