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AP Calculus BC : Calculating Limits with Algebra (including one-sided limits)

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Example Question #1 : Calculating Limits With Algebra (Including One Sided Limits)

Evaluate the following limit:

$\lim_{x\rightarrow 3^-}f(x), f(x)=\left\{\begin{matrix} x^2+1, x< 3\\ x, x\geq 3 \end{matrix}\right.$

Possible Answers:

The limit does not exist

Correct answer:

Explanation:

The limit we are given is one sided, meaning we are approaching our x value from one side; in this case, the negative sign exponent indicates that we are approaching 3 from the left side, or using values slightly less than three on approach.

This corresponds to the part of the piecewise function for values less than 3. When we substitute our x value being approached, we get

(3)^2+1=10

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AP Calculus BC : Calculating Limits with Algebra (including one-sided limits)

Study concepts, example questions & explanations for AP Calculus BC

All AP Calculus BC Resources

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Example Question #1 : Calculating Limits With Algebra (Including One Sided Limits)

All AP Calculus BC Resources

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