Difference between revisions of "2024 AMC 10A Problems/Problem 1"

Revision as of 21:45, 19 August 2024

(problem statement left as an exercise to the reader)

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) $\lim_{{x \to 0}} \frac{\sin x}{x}$

@@ Line 1: / Line 1: @@
 (problem statement left as an exercise to the reader)
-==Solution==
+If <math>x+1=2</math>, what is <math>x</math>?
-Proof left as an exercise to the reader <math>\textbf{(A)}</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>\lim_{{x \to 0}} \frac{\sin x}{x}</math>