2. Evaluate the following limits using an appropriate function and its upper or lower sums. a) limn+00 (sin + sin 2 + ...+ sin ). Hint: Use the function f(x) = sin(rx), and an appropriate partition of the interval [0, 1], then imitate the proof in the notes/video. 3n b) limn0 n + (en +en + . .+e). Hint: Choose an appropriate function, an appropri- ate partition, and then use the limit of an upper upper sum as in a).
2. Evaluate the following limits using an appropriate function and its upper or lower sums. a) limn+00 (sin + sin 2 + ...+ sin ). Hint: Use the function f(x) = sin(rx), and an appropriate partition of the interval [0, 1], then imitate the proof in the notes/video. 3n b) limn0 n + (en +en + . .+e). Hint: Choose an appropriate function, an appropri- ate partition, and then use the limit of an upper upper sum as in a).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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16.2. Thanks.
![2. Evaluate the following limits using an appropriate function and its upper or lower sums.
a) limn+0; (sin + sin 2 + ...+ sin ). Hint: Use the function f(x) = sin(rx), and
an appropriate partition of the interval [0, 1], then imitate the proof in the notes/video.
b) lim,00 (en + en +...+ en). Hint: Choose an appropriate function, an appropri-
ate partition, and then use the limit of an upper upper sum as in a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbb66fa7-7c22-4982-a22f-aaed542f65b3%2F4e3876bc-bcac-4dca-9e2a-9f85a3bb56bb%2Fa97z7ha_processed.png&w=3840&q=75)
Transcribed Image Text:2. Evaluate the following limits using an appropriate function and its upper or lower sums.
a) limn+0; (sin + sin 2 + ...+ sin ). Hint: Use the function f(x) = sin(rx), and
an appropriate partition of the interval [0, 1], then imitate the proof in the notes/video.
b) lim,00 (en + en +...+ en). Hint: Choose an appropriate function, an appropri-
ate partition, and then use the limit of an upper upper sum as in a).
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