fg is continuous

Here I show that the product of two continuous functions is continuous. I do it both by using epsilon-delta and the sequence definition of continuity. Interestingly, the proof is similar to the proof of the product rule for derivatives. Enjoy! Product of limits:    • Product of Limits   Product Rule Proof:    • Proof of the product rule   Continuity Playlist:    • Limits and Continuity   Subscribe to my channel:    / drpeyam   Check out my TikTok channel:   / drpeyam   Follow me on Instagram:   / peyamstagram   Follow me on Twitter:   / drpeyam   Teespring merch: https://teespring.com/stores/dr-peyam