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Martina J.
matematika

Dopočítanie limity

Dobrý deň, vedeli by ste mi prosím poradiť, akým spôsobom sa počíta príklad takého typu? Vopred ďakujem

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2 answers
Miroslav J.
Miroslav J. Contact
Ahoj, Martina!
Vyjadri si 3^x pred zátvorku v čitateli aj v menovateli a potom si to zjednoduš; ak nevieš, ako na to, kontaktuj ma.
Spp Miro
Ján V.
Ján V. Contact
Posielam riešenie
Comments:
Ján V.
Ospravedlňujem sa, obrázok neprešiel. Výsledok je 7/11. Ak vyberieme 3^x pred zátvorku v čitateli dostaneme, že 3^x(1-3^(-1)+3^(-2)). Ak to urobíme v menovateli máme 3^x(2^x/3^x+1+3^(-1)-3^(-2)). Teda 3^x v zlomku vypadne a ostane nám v čitateli 1-3^(-1)+3^(-2)=7/9 a v menovateli (2/3)^x+1+3^(-1)-3^(-2)=(2/3)^x+11/9. Keďže (2/3)^x ide pre x idúce do nekonečna k nule (lebo 2/3<1), tak výsledok limity je (7/9)/(11/9)=7/11.
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