Let 1 f(x) = X - - 1 A) First calculate f'(a) = lim h→0 f'(a)= (i) ƒ' ( − 2) = = (ii) ƒ'(0) = (iii) f'(2) (iv) f'(5) = fƒ'(a) in general using the official limit definition of the derivative: - f(a)) B) Then use the formula you come up with to answer the other questions: - 'f(a+h)-f(a) h
Let 1 f(x) = X - - 1 A) First calculate f'(a) = lim h→0 f'(a)= (i) ƒ' ( − 2) = = (ii) ƒ'(0) = (iii) f'(2) (iv) f'(5) = fƒ'(a) in general using the official limit definition of the derivative: - f(a)) B) Then use the formula you come up with to answer the other questions: - 'f(a+h)-f(a) h
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Let \( f(x) = \frac{1}{x - 1} \).
**A)** First, calculate \( f'(a) \) in general using the official limit definition of the derivative:
\[ f'(a) = \lim_{h \to 0} \left( \frac{f(a + h) - f(a)}{h} \right) \]
\[ f'(a) = \text{(blank space for the answer)} \]
**B)** Then use the formula you come up with to answer the other questions:
(i) \( f'(-2) = \text{(blank space for the answer)} \)
(ii) \( f'(0) = \text{(blank space for the answer)} \)
(iii) \( f'(2) = \text{(blank space for the answer)} \)
(iv) \( f'(5) = \text{(blank space for the answer)} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54e8c682-be67-4ef0-bd1d-cf8b2e543b76%2F9d44a517-ae06-433c-b6c6-f9711e19283a%2F4zcf75b_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( f(x) = \frac{1}{x - 1} \).
**A)** First, calculate \( f'(a) \) in general using the official limit definition of the derivative:
\[ f'(a) = \lim_{h \to 0} \left( \frac{f(a + h) - f(a)}{h} \right) \]
\[ f'(a) = \text{(blank space for the answer)} \]
**B)** Then use the formula you come up with to answer the other questions:
(i) \( f'(-2) = \text{(blank space for the answer)} \)
(ii) \( f'(0) = \text{(blank space for the answer)} \)
(iii) \( f'(2) = \text{(blank space for the answer)} \)
(iv) \( f'(5) = \text{(blank space for the answer)} \)
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