[Math] L’Hospital’s Rule application with raised exponents.

Question

I am having a little trouble going about:
$$\lim_{x\to \infty} \left(\frac{14x}{14x+10}\right)^{10x}$$

Using $\ln$ properties we can bring down the $10x$ exponent and have:$$\ln y=10x\ln\left(\frac{14x}{14x+10}\right)$$

And from here I get stuck trying to apply L'Hospital's Rule to find the limit.

Answer 1

Hint :

$$10x \ln \left(\frac{14x}{14x+10}\right)= \frac{\ln \left(\frac{14x}{14x+10}\right)}{\frac{1}{10x}}$$