by SuperAwesomeCaptain McFluffyPa
Last Updated October 09, 2019 15:20 PM - source

This is a tricky problem. Can anyone help me with the procedure and answer?

Evaluate $$ \lim_{h\to 0} \left( \frac{f(x+hx)}{f(x)}\right)^{1/h}, \text{for }f(x)=x. $$

https://i.stack.imgur.com/QGBNf.png

Note that you are given $f(x)=x$. With this piece of information, we can replace the functions in the given equation with their respective algebraic representations. For instance, the denominator would simply be $x$. What would the numerator look like? Now, as $h\rightarrow 0$, consider what the value inside the parenthesis tends towards, and similarly for the exponent.

October 09, 2019 15:14 PM

**Hint** Taking the logarithm, you have to calculate
$$\lim_{h\to 0} \frac{\ln(f(x+hx))- \ln(f(x))}{h}$$

That is the definition of the derivative of $\ln( f(x))$.

October 09, 2019 15:16 PM

- Serverfault Help
- Superuser Help
- Ubuntu Help
- Webapps Help
- Webmasters Help
- Programmers Help
- Dba Help
- Drupal Help
- Wordpress Help
- Magento Help
- Joomla Help
- Android Help
- Apple Help
- Game Help
- Gaming Help
- Blender Help
- Ux Help
- Cooking Help
- Photo Help
- Stats Help
- Math Help
- Diy Help
- Gis Help
- Tex Help
- Meta Help
- Electronics Help
- Stackoverflow Help
- Bitcoin Help
- Ethereum Help