4655
punti
Livello 2
LOG(2,4·x) - LOG(2,SIN(x))=
=LN(4·x)/LN(2) - LOG(2,SIN(x))=
=(LN(4) + LN(x))/LN(2) - LOG(2,SIN(x))=
=(2·LN(2) + LN(x))/LN(2) - LOG(2,SIN(x))=
=LN(x)/LN(2) - LN(SIN(x))/LN(2) + 2
LIM(LN(x)/LN(2) - LN(SIN(x))/LN(2) + 2) =2
x--> 0
97457
punti
Genius II
10469
punti
Livello 7
$ \displaystyle\lim_{x \to 0^+} [log_2 (4x) - log_2sinx] = $
$ = \displaystyle\lim_{x \to 0^+} log_2 \frac{4x}{sinx} = $
$ = \displaystyle\lim_{x \to 0^+} log_2 4 \frac{x}{sinx} = $
$ = \displaystyle\lim_{x \to 0^+} log_2 4 + log_2 \frac{x}{sinx} = 2 + 0 = 2$
12375
punti
Livello 4