ca0fd0…: “As a frigid parallelogram”

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Worked Out Examples Problem Videos

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Practice Problems: One Sided Limits

1 :

Determine if the following function is continuous at $\sage {p1piv2}$

$f(x) = \begin {cases} \sage {p1f1} & x < \sage {p1piv1}\\ \sage {p1f2} &\sage {p1piv1} \leq x < \sage {p1piv2}\\ \sage {p1f3} &\sage {p1piv2} \leq x\\ \end {cases}$

If the function is continuous at $\sage {p1piv2}$ , enter $1$ in the box. If it is not continuous at $\sage {p1piv2}$ , enter $0$ .

$\answer {\sage {p1ans}}$

Remember that in order to be continuous, you need to find the function’s value at the point of interest ( $\sage {p1piv2}$ in this case) and then find the limit from the left and from the right. All three of these values must exist and be equal for the function to be continuous at that point. As a hint, you should be using the function: $\sage {p1f2}$ for your limit from the left, and the function: $\sage {p1f3}$ for your limit from the right.