One Sided Limits Practice Problems
Problem: One Sided Limits #1
The plot of [latex]f(x)[/latex] is shown below. (Not to scale)
For each of the points given below, find [latex]\lim_{x\to a^-}f(x)[/latex], [latex]\lim_{x\to a^+}f(x)[/latex], [latex]\lim_{x\to a}f(x)[/latex], and [latex]f(a)[/latex].
1) [latex]a = 1[/latex]
2) [latex]a = 2[/latex]
3) [latex]a = 3[/latex]
4) [latex]a = 4[/latex]
Problem: One Sided Limits #2
Sketch a function which satisfies all of the following criteria:
1. [latex]\large{\lim_{x\to 4^-}f(x) = 2}[/latex]
2. [latex]\large{\lim_{x\to 4^+}f(x) = 4}[/latex]
3. [latex]\large{f(4)=}[/latex] Does not exist
4. [latex]\large{\lim_{x\to 1}f(x) = 5}[/latex]
5. [latex]\large{f(1) = 1}[/latex]
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