Exercise · ZW-LIMIT-OF-A-FUNCTION-007 · ★★☆ Intermediate
If \(f(x)=1\) for \(x<0\) and \(f(x)=2\) for \(x\ge 0\), what is \(\lim_{x\to 0} f(x)\)?
Choose one option.
Show answer
- A. It does not exist, because the one-sided limits are 1 and 2
Explanation
From the left f tends to 1 and from the right to 2. If the one-sided limits differ, the limit does not exist, even though \(f(0)=2\).
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-003 What does lim _x→ a f(x)=L mean?
- 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-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?