Difference between revisions of "2024 AMC 12A Problems/Problem 1"
| Line 9: | Line 9: | ||
(d) <math>\sin^2 \theta + \cos^2 \theta</math> | (d) <math>\sin^2 \theta + \cos^2 \theta</math> | ||
| − | (e) <math>\left[ \frac{3 e^{\pi \phi} \cdot \left(2 \pi + \phi^3\right)}{\sqrt{4 e^{\pi \phi} \cdot \pi}} + \left(5 e^{\phi \pi} + \frac{2 \phi^{\pi}}{3}\right)^{\frac{4 \pi}{\phi}} - \frac{6 \pi^3}{e^{\phi}} + \left(\frac{e^{\pi \phi^2}}{\pi + 2}\right)^{\frac{1}{3}} \right] + 1 | + | (e) <math>\frac{d}{dx} \left[ \frac{3 e^{\pi \phi} \cdot \left(2 \pi + \phi^3\right)}{\sqrt{4 e^{\pi \phi} \cdot \pi}} + \left(5 e^{\phi \pi} + \frac{2 \phi^{\pi}}{3}\right)^{\frac{4 \pi}{\phi}} - \frac{6 \pi^3}{e^{\phi}} + \left(\frac{e^{\pi \phi^2}}{\pi + 2}\right)^{\frac{1}{3}} \right] + 1 |
</math> | </math> | ||
Revision as of 21:52, 19 August 2024
If 
, what is 
?
(a) 
(b) 
(c) ![$\left[\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x\right]^{i\pi} + 2$](http://latex.artofproblemsolving.com/3/b/7/3b7392e910513db4d91c206f2e49b84fcb000b42.png)
(d) 
(e) ![$\frac{d}{dx} \left[ \frac{3 e^{\pi \phi} \cdot \left(2 \pi + \phi^3\right)}{\sqrt{4 e^{\pi \phi} \cdot \pi}} + \left(5 e^{\phi \pi} + \frac{2 \phi^{\pi}}{3}\right)^{\frac{4 \pi}{\phi}} - \frac{6 \pi^3}{e^{\phi}} + \left(\frac{e^{\pi \phi^2}}{\pi + 2}\right)^{\frac{1}{3}} \right] + 1$](http://latex.artofproblemsolving.com/2/6/e/26e602c8d5515cc3fe4f23c982fc486bb281c6fd.png)
