Difference between revisions of "2024 AMC 12A Problems/Problem 1"
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If <math>x+1=2</math>, what is <math>x</math>? | If <math>x+1=2</math>, what is <math>x</math>? | ||
| − | (a) <math>1</math> | + | (a) <math>1</math> |
| + | |||
| + | (b) <math>\frac{1}{2} \int_{0}^{2} x \, dx</math> | ||
| + | |||
| + | (c) <math>\left[\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x\right]^{i\pi} + 2</math> | ||
| + | |||
| + | (d) <math>\sin^2 \theta + \cos^2 \theta</math> | ||
| + | |||
| + | (e) <math>\frac{d}{d\theta}\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> | ||
Latest revision as of 22:53, 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) ![$\frac{d}{d\theta}\left[ \frac{3 e^{\pi \phi} \cdot \left(2 \pi + \phi^3\right)}{\sqrt{4 e^{\pi \phi} \cdot \pi}} + \left(5 e^{\phi \pi} + \frac{2 \phi^{\pi}}{3}\right)^{\frac{4 \pi}{\phi}} - \frac{6 \pi^3}{e^{\phi}} + \left(\frac{e^{\pi \phi^2}}{\pi + 2}\right)^{\frac{1}{3}} \right] + 1$](http://latex.artofproblemsolving.com/7/9/5/7958ee4e9aa5ba5726de02a344f567d8b13a7021.png)
