et f(r) be the function 107² +9r+ 5. low the steps below to use the formal definition of the derivative lim h 0 ostitute and evaluate: f(r+h) = mplify f(r + h) − f(r) = er the simplified difference quotient f(r+h)-f(r) h er your answer for (AFTER computing the limit.) df dr to find dr f(r+h)-f(r) h (BEFORE computing the limit.) (Note: simplify to the point where you could evaluate the limit algebraically, i.e. until you are no longer dividing by 0.)
et f(r) be the function 107² +9r+ 5. low the steps below to use the formal definition of the derivative lim h 0 ostitute and evaluate: f(r+h) = mplify f(r + h) − f(r) = er the simplified difference quotient f(r+h)-f(r) h er your answer for (AFTER computing the limit.) df dr to find dr f(r+h)-f(r) h (BEFORE computing the limit.) (Note: simplify to the point where you could evaluate the limit algebraically, i.e. until you are no longer dividing by 0.)
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.
Chapter3: The Derivative
Section3.5: Graphical Differentiation
Problem 2E
Related questions
Question
![---
**Problem:**
Let \( f(r) \) be the function \( 10r^2 + 9r + 5 \).
Follow the steps below to use the formal definition of the derivative \(\lim_{{h \to 0}} \frac{{f(r + h) - f(r)}}{h}\) to find \(\frac{{df}}{{dr}}\).
---
1. **Substitute and evaluate:**
\[ f(r + h) = \quad \underline{\hspace{400px}} \]
2. **Simplify:**
\[ f(r + h) - f(r) = \quad \underline{\hspace{400px}} \]
3. **Enter the simplified difference quotient:** (BEFORE computing the limit.)
\[ \frac{{f(r + h) - f(r)}}{h} = \quad \underline{\hspace{400px}} \]
*(Note: simplify to the point where you could evaluate the limit algebraically, i.e., until you are no longer dividing by 0.)*
4. **Enter your answer for \(\frac{{df}}{{dr}}\)** (AFTER computing the limit.)
\[ \frac{{df}}{{dr}} = \quad \underline{\hspace{400px}} \]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F114d112a-89da-40ea-8ec8-a25f26317aff%2F975aa1a5-0f16-4d5e-9c35-e6ad3dd17b67%2Fxw1fbv_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Problem:**
Let \( f(r) \) be the function \( 10r^2 + 9r + 5 \).
Follow the steps below to use the formal definition of the derivative \(\lim_{{h \to 0}} \frac{{f(r + h) - f(r)}}{h}\) to find \(\frac{{df}}{{dr}}\).
---
1. **Substitute and evaluate:**
\[ f(r + h) = \quad \underline{\hspace{400px}} \]
2. **Simplify:**
\[ f(r + h) - f(r) = \quad \underline{\hspace{400px}} \]
3. **Enter the simplified difference quotient:** (BEFORE computing the limit.)
\[ \frac{{f(r + h) - f(r)}}{h} = \quad \underline{\hspace{400px}} \]
*(Note: simplify to the point where you could evaluate the limit algebraically, i.e., until you are no longer dividing by 0.)*
4. **Enter your answer for \(\frac{{df}}{{dr}}\)** (AFTER computing the limit.)
\[ \frac{{df}}{{dr}} = \quad \underline{\hspace{400px}} \]
---
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,