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In this lesson, we will learn how to interpret the formal epsilon–delta definition of a limit and find the value of delta for a given epsilon.

Q1:

Find the largest 𝛿>0 such that if |𝑥−5|<𝛿, then |||1𝑥−15|||<110. Give your answer as a fraction.

Q2:

Find the largest 𝛿>0 such that if |𝑥−5|<𝛿, then |||1𝑥−15|||<𝜀. Give your answer as a fraction involving 𝜀.

Q3:

Find the largest 𝑎>0 such that if |𝑥−𝑎|<𝑎, then |||1𝑥−1𝑎|||<𝜀. Give your answer as a fraction involving 𝜀 and 𝑎.

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