Grenzwertberechnung
Wenn Sie auf “Auswerten” clicken wird die Funktion
f
(
x
,
n
)
=
n
x
−
n
−
x
n
x
+
n
−
x
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm aabaGaamiEaiaacYcacaWGUbaacaGLOaGaayzkaaGaeyypa0ZaaSaa aeaacaWGUbWaaWbaaSqabeaaqaaaaaaaaaWdbiaadIhaaaGcpaGaey OeI0IaamOBamaaCaaaleqabaWdbiabgkHiTiaadIhaaaaak8aabaGa amOBamaaCaaaleqabaWdbiaadIhaaaGcpaGaey4kaSIaamOBamaaCa aaleqabaWdbiabgkHiTiaadIhaaaaaaaaa@48D9@
graphisch dargestellt.
Frage:
Was bedeuten
lim
n
→
∞
f
(
x
,
n
)
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGHEisPaeqaaOGa amOzamaabmaabaGaamiEaiaacYcacaWGUbaacaGLOaGaayzkaaaaaa@426F@
,
lim
x
→
∞
f
(
x
,
n
)
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcqGHEisPaeqaaOGa amOzamaabmaabaGaamiEaiaacYcacaWGUbaacaGLOaGaayzkaaaaaa@4279@
und
lim
x
→
0
f
(
x
,
n
)
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaaabeaakiaa dAgadaqadaqaaiaadIhacaGGSaGaamOBaaGaayjkaiaawMcaaaaa@41C2@
?