MATH122 Learning Portfolio 1A

One topic from Unit 1 that I feel most confident about is Derivatives Review. I practiced derivatives a lot in previous classes, so it feels familiar and manageable now. I understand the rules like product, quotient, and chain rule, and I can quickly recognize which one applies. My advice to students struggling would be to write out each step carefully rather than skipping mental shortcuts, because small mistakes add up. I also recommend reviewing old derivative rules since they keep appearing in new problems. On the exam, I predict Judy might give a f

unction with multiple rules combined—like a quotient inside a chain rule—to test if we can apply them together.

Effort

The topic I struggled with at first but now feel more confident about is L’Hopital’s Rule. At the beginning, I mixed up when to apply it and sometimes forgot to check the indeterminate form first. With practice, I learned to pause and confirm the limit is actually in the form

0/0 or ∞/∞ before applying the rule. Working through homework problems helped me see patterns in how derivatives simplify the fraction. My advice to other students is to be patient and not rush—checking the form saves mistakes. Your professor might ask us to evaluate a tricky limit that requires applying L’Hôpital’s Rule more than once or combining it with algebraic simplification.

Areas of Growth

The topic I struggle with the most from Unit 1 is Improper Integrals. I find it hard because I sometimes forget how to set up the limit properly, especially when infinity or discontinuities are involved. I also get mixed up between when the integral converges and when it diverges. My challenge is slowing down enough to carefully evaluate the limit and not just assume it converges. To improve, I plan to practice more examples and check solutions step by step. you might ask a question where the integral has an infinite bound or an asymptote at zero, and we’d need to prove whether it converges or diverges.