Many students find it hard to understand limits at infinity and vertical asymptotes. Here are some common misunderstandings:
Thinking Limits Are Always There: Some students believe every function gets close to a certain number as ( x ) gets really big. This is not true for functions like ( f(x) = \frac{1}{x} ).
Mixing Up Asymptotes: Vertical asymptotes show where a function behaves in an undefined way. However, some students mistakenly think these asymptotes mean a limit exists.
Mistaking Infinity: Infinity isn't a real number. Students might think ( f(x) \to \infty ) means ( f(x) = \infty ), which isn’t right.
To help clear up these misunderstandings, practicing problems, using visual aids, and having deeper conversations about how functions behave can make things easier to understand.
Many students find it hard to understand limits at infinity and vertical asymptotes. Here are some common misunderstandings:
Thinking Limits Are Always There: Some students believe every function gets close to a certain number as ( x ) gets really big. This is not true for functions like ( f(x) = \frac{1}{x} ).
Mixing Up Asymptotes: Vertical asymptotes show where a function behaves in an undefined way. However, some students mistakenly think these asymptotes mean a limit exists.
Mistaking Infinity: Infinity isn't a real number. Students might think ( f(x) \to \infty ) means ( f(x) = \infty ), which isn’t right.
To help clear up these misunderstandings, practicing problems, using visual aids, and having deeper conversations about how functions behave can make things easier to understand.