Chapter 2: Q 2 (page 187)
Use the definition of the derivative to show that role="math" localid="1648386605099" .
Chapter 2: Q 2 (page 187)
Use the definition of the derivative to show that role="math" localid="1648386605099" .
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Get started for freeProve, in two ways, that the power rule holds for negative integer powers
a) by using the definition of the derivative
b) by using thedefinition of the derivative
Each 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 derivative to directly prove the differentiation rules for constant and identity function
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
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 ?
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