Solution: One Sided Limits #2
Solution: 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]
There are many ways to solve this problem and any kind of function can be drawn, as long as it satisfies the given criteria. A possible graph could look like:
The graph of [latex]f(x)[/latex] shown satisfies all of the given criteria. We can see that the limit as the function approaches 4 from the left and right side is 2 and 4 respectively.
Also, we can see that there is no defined value at x = 4, as indicated by the two holes. It also clear that the function value at x = 1 is 1, as shown by the solid dot. Finally, the limit as z approaches 1, from both sides, is shown to be 5.
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Solution: 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]
There are many ways to solve this problem and any kind of function can be drawn, as long as it satisfies the given criteria. A possible graph could look like:
The graph of [latex]f(x)[/latex] shown satisfies all of the given criteria. We can see that the limit as the function approaches 4 from the left and right side is 2 and 4 respectively.
Also, we can see that there is no defined value at x = 4, as indicated by the two holes. It also clear that the function value at x = 1 is 1, as shown by the solid dot. Finally, the limit as z approaches 1, from both sides, is shown to be 5.
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