5. Assume fn :D → R converges uniformly to f and gn: D → R converges uniformly to g. Prove that (fngn) converges uniformly to fg.
5. Assume fn :D → R converges uniformly to f and gn: D → R converges uniformly to g. Prove that (fngn) converges uniformly to fg.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.4: Improper Integrals
Problem 37E
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![5. Assume fn :D → R converges uniformly to f and gn: D → R converges
uniformly to g. Prove that (fngn) converges uniformly to fg.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F53e2d028-8e28-453c-8f8b-9b649396dc23%2Flr17mcc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Assume fn :D → R converges uniformly to f and gn: D → R converges
uniformly to g. Prove that (fngn) converges uniformly to fg.
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