- Topic
- Continuity
- Difficulty
- Standard
- Suggested time
- 4 min
- Marks
- 2
Continuity practice question 11
Find the value of the constant that makes continuous everywhere.
Each piece is a polynomial, so the only place continuity can fail is the join at .
Set the left-hand limit at 2 equal to the right-hand limit at 2 and solve for .
A fraction, or a decimal to two decimal places.
Theory UBC Math 100 §2.3CLP-1 §1.6Key results
Worked solution
Strategy
Polynomials are continuous, so only the join matters. Continuity at the join is one equation: the two pieces must agree there.
Working
From the left, the first piece applies.
From the right, the second piece applies, and it also gives f(2).
Continuity at 2 forces the two to agree.
Answer
The answer is c equals seven thirds, about 2.33.
Check
With c = 7/3 both pieces meet at height 25/3 ≈ 8.33 when x = 2: 28/3 − 1 = 6 + 7/3.
Where this goes wrong
Substituting x = 2 into only one piece, or setting the pieces equal as functions rather than at the single point x = 2. The condition is about the values at the join only.
Leans on
One-sided limits of a piecewise function, from Limits
Try a similar question
Find the value of that makes continuous at .Saved in this browser only.