r(t) = tan (t – 2/7) + 0.1t² A student is asked to write the limit definition of the derivative at t = 7, and to illustrate how the graphical interpretation of r'(7) follows from this limit. The lines of their solution are numbered 1-10 below. 1. We illustrate the situation below. r(t) h. n-n+h 2. 3. By the limit definition of the derivative, tan(7 + h – 2/m) + 0.1(7² + h²) – tan(7 – 2/7) – 0.17² 4. r'(7) = lim,0 h 5. This limit above is equal to a number. 6. Call the value of this limit A. 7. The point 7 + h is to the right of T (since h is positive). 8. A is equal to the secant line between r and T + h. 9. Taking the limit as h goes to 0 corresponds to taking secant lines over smaller and smaller intervals [7, 7 + h]. 10. When h is very small (as shown) the secant line will be equal to the tangent line. In the table on the next page, write the numbers of four steps where the student made an error
r(t) = tan (t – 2/7) + 0.1t² A student is asked to write the limit definition of the derivative at t = 7, and to illustrate how the graphical interpretation of r'(7) follows from this limit. The lines of their solution are numbered 1-10 below. 1. We illustrate the situation below. r(t) h. n-n+h 2. 3. By the limit definition of the derivative, tan(7 + h – 2/m) + 0.1(7² + h²) – tan(7 – 2/7) – 0.17² 4. r'(7) = lim,0 h 5. This limit above is equal to a number. 6. Call the value of this limit A. 7. The point 7 + h is to the right of T (since h is positive). 8. A is equal to the secant line between r and T + h. 9. Taking the limit as h goes to 0 corresponds to taking secant lines over smaller and smaller intervals [7, 7 + h]. 10. When h is very small (as shown) the secant line will be equal to the tangent line. In the table on the next page, write the numbers of four steps where the student made an error
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![r(t) = tan (t – 2/T) + 0.1t2
A student is asked to write the limit definition of the derivative at t = 7, and to illustrate
how the graphical interpretation of r' (7) follows from this limit. The lines of their solution are
numbered 1-10 below.
1. We illustrate the situation below.
r(t)
h
TI-n+h
2.
3. By the limit definition of the derivative,
tan(7 +h – 2/T) + 0.1(n² + h²) – tan(7 – 2/7) – 0.17²
4. r'(T) = lim¬→0
h
5. This limit above is equal to a number.
6. Call the value of this limit A.
7. The point T + h is to the right of 7 (since h is positive).
8. A is equal to the secant line between 7 and T + h.
9. Taking the limit as h goes to 0 corresponds to taking secant lines over smaller and smaller
intervals (T, 7 + h].
10. When h is very small (as shown) the secant line will be equal to the tangent line.
In the table on the next page, write the numbers of four steps where the student made an error](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2265aced-351c-4f54-ac17-63def3496631%2F911d39ce-337a-4e5e-a959-1a25f8506096%2Fxt7862zbp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:r(t) = tan (t – 2/T) + 0.1t2
A student is asked to write the limit definition of the derivative at t = 7, and to illustrate
how the graphical interpretation of r' (7) follows from this limit. The lines of their solution are
numbered 1-10 below.
1. We illustrate the situation below.
r(t)
h
TI-n+h
2.
3. By the limit definition of the derivative,
tan(7 +h – 2/T) + 0.1(n² + h²) – tan(7 – 2/7) – 0.17²
4. r'(T) = lim¬→0
h
5. This limit above is equal to a number.
6. Call the value of this limit A.
7. The point T + h is to the right of 7 (since h is positive).
8. A is equal to the secant line between 7 and T + h.
9. Taking the limit as h goes to 0 corresponds to taking secant lines over smaller and smaller
intervals (T, 7 + h].
10. When h is very small (as shown) the secant line will be equal to the tangent line.
In the table on the next page, write the numbers of four steps where the student made an error
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