Chapter 2: Q. 5 (page 183)
Explain why the limitsandare the same for any function . (Hint: Consider the substitution .)
Short Answer
and are the same for any function.
Chapter 2: Q. 5 (page 183)
Explain why the limitsandare the same for any function . (Hint: Consider the substitution .)
and are the same for any function.
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Get started for freeEach graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line that passes through the point and is parallel to the tangent line to at .
Differentiate in three ways. When you have completed all three parts, show that your three answers are the same:
(a) with the chain rule
(b) with the product rule but not the chain rule
(c) without the chain or product rules.
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Use the definition of the derivative to find for each function in Exercises 34-59
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