Practice question · Sort into groups
Sort each limit by its value.
Groups: Limit is 0 · Limit is 2 · Limit does not exist
- (x squared - 1)/(x - 1) as x approaches 1
- 1/x as x approaches 0
- 3x as x approaches 0
- (x squared - 2x)/(x - 2) as x approaches 2
Hints
- Try substitution first; only reach for factoring when it gives 0/0.
- The fourth item factors as x(x - 2) over x - 2.
Show the answer
Limit is 0: 3x as x approaches 0
Limit is 2: (x squared - 1)/(x - 1) as x approaches 1, (x squared - 2x)/(x - 2) as x approaches 2
Limit does not exist: 1/x as x approaches 0
Why
Items 2 and 4 both simplify and evaluate to 2; items 1 and 6 need only substitution. The two failures fail for different reasons: 1/x blows up without settling anywhere, while the absolute-value quotient settles on two DIFFERENT values from the two sides.
Practise Limits
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.