Chapter 10: Q. 89 (page 777)
Use limit rules and the continuity of power functions to prove that every polynomial function is continuous everywhere.
Short Answer
The polynomial function is continuous at.
Chapter 10: Q. 89 (page 777)
Use limit rules and the continuity of power functions to prove that every polynomial function is continuous everywhere.
The polynomial function is continuous at.
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In Exercises 37–42, find and find the unit vector in the direction of v.
Use the Intermediate Value Theorem to prove that every cubic function has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.
Prove the first part of Theorem (a): If , then . (Hint: Given , choose . Then show that for it must follow that .)
In Exercises 22–29 compute the indicated quantities when
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