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Chapter 1: Q. 4 (page 119)
Explain what it means for a function to be continuous at a point , with a sentence that includes the words 鈥渁pproaches鈥� and 鈥渧alue.鈥�
Functionapproaches towards and the value of function at that point is.
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In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.
Calculate each of the limits:
.
Write a delta鈥揺psilon proof that proves that is continuous on its domain. In each case, you will need to assume that 未 is less than or equal to .
Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.
In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.
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