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3 cards from this section. Quick, good the night before a test.
Determine if the limit exists: lim f(x) as x approaches 2 for f(x) = {2 if x < 2, 3 if x > 2}
Evaluate from the left and right.
Evaluate lim (1/x) as x approaches 0.
Consider what happens as x nears zero.
If the left-side limit is 2 and the right-side limit is 3 as x approaches 1, does the limit exist?
Remember: Left != Right means DNE.
True or False: The limit of sin(1/x) as x approaches 0 exists.
Think about the behavior of the function around zero.
Analyze the limit of f(x) = (x^2 - 1)/(x - 1) as x approaches 1. Why is there a need for simplification?
Factor first before direct substitution.
Evaluate the limit lim f(x) as x approaches 0 for f(x) = 1/x if x approaches from the left and right. Discuss your findings.
Consider the directional limits separately.
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