In a time of t seconds, a particle moves a distance of s meters from its starting point, where s(t) = 3t2 − 1. 1. Complete the following table of values. Do not round your solutions. t 2 2.001 2.01 2.1 s(t) 2. Find the average rate of change between t = 2 and t = 2 + ∆t if: i. ∆t = 0.1 ii. ∆t = 0.01 iii. ∆t = 0.001 3. As we choose a smaller and smaller interval around t = 2 the average rate of change appears to be getting closer and closer to the numerical value _____ . So we estimate the instantaneous rate of change at t = 2 to be _____ m/sec. 4. Find s'(t) using rules of differentiation. 5. Use s'(t) to find the exact value of s'(2)
In a time of t seconds, a particle moves a distance of s meters from its starting point, where s(t) = 3t2 − 1. 1. Complete the following table of values. Do not round your solutions. t 2 2.001 2.01 2.1 s(t) 2. Find the average rate of change between t = 2 and t = 2 + ∆t if: i. ∆t = 0.1 ii. ∆t = 0.01 iii. ∆t = 0.001 3. As we choose a smaller and smaller interval around t = 2 the average rate of change appears to be getting closer and closer to the numerical value _____ . So we estimate the instantaneous rate of change at t = 2 to be _____ m/sec. 4. Find s'(t) using rules of differentiation. 5. Use s'(t) to find the exact value of s'(2)
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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In a time of t seconds, a particle moves a distance of s meters from its starting point, where s(t) = 3t2 − 1.
1. Complete the following table of values. Do not round your solutions.
| t | 2 | 2.001 | 2.01 | 2.1 |
| s(t) |
2. Find the average rate of change between t = 2 and t = 2 + ∆t if:
i. ∆t = 0.1
ii. ∆t = 0.01
iii. ∆t = 0.001
3. As we choose a smaller and smaller interval around t = 2 the average rate of change appears to be getting closer and closer to the numerical value _____ . So we estimate the instantaneous rate of change at t = 2 to be _____ m/sec.
4. Find s'(t) using rules of
5. Use s'(t) to find the exact value of s'(2).
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