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
Related questions
Question
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).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
