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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The tangent line to at
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.
Prove that if f is a quadratic polynomial function then the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows
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.
27.
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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