existence and value of the limit of a function
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1. Does the existence and value of the limit of a function f(x) as x approaches x_o ever depend on what happens at x = x_o? Explain and give examples.
2. What does it mean for a function to be continuous? Give examples to illustrate the fact that a function that is not continuous on its entire domain may still be continuous on selected intervals within the domain.
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The existence and value of the limit of a function are depicted.
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1. Does the existence and value of the limit of a function f(x) as x approaches x_o ever depend on what happens at x = x_o? Explain and give examples.
Solution:
The definition of limit is
Let f be a function from the real numbers (R) to the real numbers (R), and let x be a real number. Lim(x->x ) f(x) = L which means that for every > 0, there is a > 0, such that if > |x - x | > 0, then > |f(x) - L|.
From the above definition it follows that the existence and value of the limit of a ...
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