^x}{x} "\displaystyle\: \lim_{x \to 0}\frac{4^x-(\frac 12)^x}{x}")
is gelijk aan
|
A. ln 2 |
|---|
| B. 2.ln 2 |
| C. 3.ln 2 |
| D. 4.ln 2 |
| E. 0 |
[ 6-6822 - op net sinds 11.12.11-(E)-6.11.2024 ]
Translation in E N G L I S H
^x}{x} "\displaystyle\: \lim_{x \to 0}\frac{4^x-(\frac 12)^x}{x}")
equals
|
A. ln 2 |
|---|
| B. 2 (ln 2) |
| C. 3 (ln 2) |
| D. 4 (ln 2) |
| E. 0 |
Oplossing - Solution
\(\displaystyle\: \lim_{x \to 0}\frac{4^x-(\frac 12)^x}{x}\left ( =\frac{1-1}{0} \right )\overset{H}{=}\displaystyle\: \lim_{x \to 0}\frac{4^x.\ln 4-(\frac 12)^x.\ln (\frac12)}{1}\\=4^0.\ln 4-(\frac 12)^0.\ln(\frac 12)=\ln 4 + \ln 2 = 2.\ln 2 + \ln 2 = 3.\ln 2\)
