Very hard calculus questions
Question 1: \[ \text{Evaluate } \lim_{x \to 0} \frac{\sin(x) – x}{x^3}. \] \[ \text{(a) } -\frac{1}{6}, \quad \text{(b) } 0, \quad \text{(c) } \frac{1}{6}, \quad \text{(d) } \frac{1}{2} \] Answer: A Question 2: \[ \text{Evaluate } \int_0^\infty \frac{x^2}{e^x – 1} dx. \] \[ \text{(a) } \frac{\pi^2}{6}, \quad \text{(b) } \frac{\pi^2}{3}, \quad \text{(c) } \frac{\pi^2}{2}, \quad … Read more