Chapter 2: Q 2. (page 237)
Translate expressions written in Leibniz notation to “prime” notation, and vice versa.
Chapter 2: Q 2. (page 237)
Translate expressions written in Leibniz notation to “prime” notation, and vice versa.
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Get started for freeFind the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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 hits the ground, with
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.
For each function and interval localid="1648297458718" in Exercises localid="1648297462718" , use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" . Then apply Newton’s method to approximate that root.
localid="1648297471865"
A tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
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