Exercise · ZW-LIMIT-OF-A-FUNCTION-003 · ★☆☆ Basic
What does \(\lim_{x\to a} f(x)=L\) mean?
Choose one option.
Show answer
- A. The values of \(f(x)\) approach \(L\) as \(x\) approaches \(a\)
Explanation
The limit describes the value that outputs approach as \(x\) nears \(a\). It says nothing about the exact value at \(a\).
Review the concept: Limit of a function
The limit of \(f\) as \(x\) approaches \(a\) is \(L\) if \(f(x)\) gets as close to \(L\) as we like when \(x\) is taken sufficiently close to \(a\), regardless of what happens at \(x=a\).
\[\lim_{x\to a} f(x)=L\]
More practice problems: limit of a function
- ZW-LIMIT-OF-A-FUNCTION-001 If lim _x→ 2 f(x)=5, what can be stated for sure?
- ZW-LIMIT-OF-A-FUNCTION-002 Which statement about the limit of f at a is correct?
- ZW-LIMIT-OF-A-FUNCTION-004 What is lim _x→ 3 2x?
- ZW-LIMIT-OF-A-FUNCTION-005 What is lim _x→ 2(x^2-4)/(x-2)?
- ZW-LIMIT-OF-A-FUNCTION-006 What is lim _x→ 0(sin x)/(x)?
- ZW-LIMIT-OF-A-FUNCTION-007 If f(x)=1 for x<0 and f(x)=2 for x≥ 0, what is lim _x→ 0 f(x)?
- ZW-LIMIT-OF-A-FUNCTION-008 What is lim _x→ 1(x^3-1)/(x-1)?
- ZW-LIMIT-OF-A-FUNCTION-009 What is lim _x→ a c if c is a constant?