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Lesson Worksheet: Formal Definition of Infinite Limits and Limits at Infinity Mathematics
In this worksheet, we will practice interpreting the formal epsilon–delta definition of limits at infinity and limits that tend to infinity as x approaches a certain value.
Q1:
As we prove that , what should be the relation between and such that and ?
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Q2:
Suppose that . Using the formal definition of limits, find the interval of centered around so that the inequality is satisfied.
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Q3:
Find as a function of for a proof that .
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Q4:
Given that , find the value of such that for any , , with .
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Q5:
Find as a function of to prove that .
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