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Chapter 2: Q. 13 (page 233)
The figure that follows at the left shows the graphs of For each of the statements that follows, explain graphically why the statement is true. Then justify the statement algebraically, using the definitions of the hyperbolic functions.
The expressions are proved.
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Suppose and . Use the chain rule to find role="math" localid="1648356625815" without first finding the formula for .
Each graph in Exercises 31鈥�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 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.
A bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
When the bowling ball is first dropped, with
use the definition of derivative to directly prove the differentiation rules for constant and identity function
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