2024 AMC 12A Problems/Problem 1

If $x+1=2$ , what is $x$ ?

(a) $1$

(b) $\frac{1}{2} \int_{0}^{2} x \, dx$

(c) $\left[\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x\right]^{i\pi} + 2$

(d) $\sin^2 \theta + \cos^2 \theta$

(e) $\frac{d}{d\theta}\left[ \frac{3 e^{\pi \phi} \cdot \left(2 \pi + \phi^3\right)}{\sqrt{4 e^{\pi \phi} \cdot \pi}} + \left(5 e^{\phi \pi} + \frac{2 \phi^{\pi}}{3}\right)^{\frac{4 \pi}{\phi}} - \frac{6 \pi^3}{e^{\phi}} + \left(\frac{e^{\pi \phi^2}}{\pi + 2}\right)^{\frac{1}{3}} \right] + 1$

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2024 AMC 12A Problems/Problem 1