Problem 1
T/F: If \(\lim _{x \rightarrow 5} f(x)=\infty,\) then we are implicitly stating that the limit exists.
Problem 1
What is wrong with the following "definition" of a limit? "The limit of \(f(x)\), as \(x\) approaches \(a\), is \(K^{\prime \prime}\) means that given any \(\delta>0\) there exists \(\varepsilon>0\) such that whenever \(|f(x)-K|<\varepsilon,\) we have \(|x-a|<\delta\)
Problem 1
Explain in your own words, without using \(\varepsilon-\delta\) formality, why \(\lim _{x \rightarrow c} b=b\)
Problem 1
What are the three ways in which a limit may fail to exist?
Problem 1
In your own words, describe what it means for a function to be continuous.
Problem 1
In your own words, what does it mean to "find the limit of \(f(x)\) as \(x\) approaches \(3^{\prime \prime} ?\)
Problem 2
An expression of the form \(\frac{0}{0}\) is called ______.
Problem 2
In your own words, describe what the Intermediate Value Theorem states.
Problem 2
T/F: If \(\lim _{x \rightarrow \infty} f(x)=5,\) then we are implicitly stating that the limit exists.
Problem 2
Explain in your own words, without using \(\varepsilon-\delta\) formality, why \(\lim _{x \rightarrow c} b=b\)
