Would someone mind verifying this?
$ \lim_{x\to \infty} \frac{2 \cdot 3^{5x} + 5}{3^{5x} + 2^{5x}} = \lim_{x\to \infty} \frac{3^{5x}(2 + \frac{5}{3^{5x}})}{3^{5x}(1 + (\frac{2}{3})^{5x})} = \lim_{x\to \infty} \frac{2 + \frac{5}{3^{5x}}}{1 + (\frac{2}{3})^{5x}} = \frac{2 + \frac{5}{3^{5(\infty)}}}{1 + (\frac{2}{3})^{5(\infty)}} = \frac{2 + 0}{1 + 0} = 2 $
$ \lim_{x\to 0} \frac{e^{2x}-\pi^{x}}{sin(3x)} = \lim_{x\to 0} \frac{2e^{2x}-\pi^{x} ln(\pi)}{3cos(3x)} = \frac{2e^{2(0)}-\pi^{(0)} ln(\pi)}{3cos(3(0))} = \frac{2\cdot 1 - 1\cdot ln(\pi)}{3\cdot1} = \frac{2-ln(\pi)}{3} $