(Solved): Exam 3 Question 3A (a) Determine if \( \int_{-\infty}^{0} x e^{x} d x \) converges. (Hint: you will ...

Exam 3 Question 3A (a) Determine if \( \int_{-\infty}^{0} x e^{x} d x \) converges. (Hint: you will need to use l'Hopital's Rule as part of your solution). (b) Find \( \int_{0}^{3} \frac{1}{x-1} d x \) using the limit definition of the improper integral. Your solutions must include limits and complete reasoning.