Chapter 2: Q. 3 (page 232)
What limit facts and trigonometric identities are used in
the proof that
Short Answer
limit facts and sum identity for the sine are used in the proof of
Chapter 2: Q. 3 (page 232)
What limit facts and trigonometric identities are used in
the proof that
limit facts and sum identity for the sine are used in the proof of
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Get started for freeTaking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
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Use the limit just defined to calculate the exact slope of the tangent line toat
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 the derivative to find for each function f in Exercises 39-54
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
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.
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