- #1
SYoungblood
- 64
- 1
Homework Statement
Hello, thank you in advance for all help. This is a limit problem that is giving me a particularly hard time.
Homework Equations
For what values of a and b is f(x) continuous at every x? In other words, how to unify the three parts of a piecewise function so that there are no holes or jumps in the function?
f(x) = { (i) -2 for values less than or equal to -1; (ii) ax - b for values of -1 < x < 1; and (iii) 3 for values greater than or equal to 1?
The Attempt at a Solution
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The lefthand limit for (i) as x approaches -1 and the righthand limit for (iii) as x approaches 1 are fairly straightforward. (ii) is a polynomial, so the limit is continuous over that interval. In theory, and most certainly in practice, there are values for the limits as x approaches -1 and 1 that make all of f(x) continuous. However, I cannot seem to reconcile how to substitute values for x to find a and b. If I set ax - b = -1, or 1, the way I see it, I have two variables and cannot account for both.
Thank you again,
SY