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 freeUse (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
24.
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.
Velocity is the derivative of position . It is also true that acceleration (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function , what are the units of ? What are the units and real-world interpretation of ? What are the units and real-world interpretations of ?
The following reciprocal rules tells us hoe to differentiate the reciprocal of a function
Prove this using
a) definition of the derivative
b) by using the quotient rule
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
23.
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