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# Unit 1: Limits and continuity

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## About this unit

Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point matches the function's value at that point. These simple yet powerful ideas play a major role in all of calculus.

### Practice

- Limits introGet 3 of 4 questions to level up!

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### Practice

- Estimating limit values from graphsGet 3 of 4 questions to level up!
- One-sided limits from graphsGet 3 of 4 questions to level up!
- Connecting limits and graphical behaviorGet 3 of 4 questions to level up!

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### Practice

- Creating tables for approximating limitsGet 3 of 4 questions to level up!
- Estimating limits from tablesGet 3 of 4 questions to level up!
- One-sided limits from tablesGet 3 of 4 questions to level up!

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- Limits of combined functions: sums and differencesGet 3 of 4 questions to level up!
- Limits of combined functions: products and quotientsGet 3 of 4 questions to level up!
- Limits of composite functionsGet 3 of 4 questions to level up!

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### Practice

- Limits by direct substitutionGet 3 of 4 questions to level up!
- Direct substitution with limits that don't existGet 3 of 4 questions to level up!
- Limits of trigonometric functionsGet 3 of 4 questions to level up!
- Limits of piecewise functionsGet 3 of 4 questions to level up!

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### Practice

- Limits by factoringGet 3 of 4 questions to level up!
- Limits using conjugatesGet 3 of 4 questions to level up!
- Limits using trig identitiesGet 3 of 4 questions to level up!

### Practice

- Conclusions from direct substitution (finding limits)Get 3 of 4 questions to level up!
- Next steps after indeterminate form (finding limits)Get 3 of 4 questions to level up!
- Strategy in finding limitsGet 3 of 4 questions to level up!

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### Practice

- Classify discontinuitiesGet 3 of 4 questions to level up!

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### Practice

- Continuity at a point (graphical)Get 3 of 4 questions to level up!
- Continuity at a point (algebraic)Get 3 of 4 questions to level up!

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- Continuity over an intervalGet 3 of 4 questions to level up!
- Continuity and common functionsGet 3 of 4 questions to level up!

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- Removable discontinuitiesGet 3 of 4 questions to level up!

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### Practice

- Infinite limits: graphicalGet 3 of 4 questions to level up!
- Infinite limits: algebraicGet 3 of 4 questions to level up!

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### Practice

- Limits at infinity: graphicalGet 3 of 4 questions to level up!
- Limits at infinity of quotientsGet 5 of 7 questions to level up!
- Limits at infinity of quotients with square rootsGet 3 of 4 questions to level up!

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- Using the intermediate value theoremGet 3 of 4 questions to level up!
- Justification with the intermediate value theoremGet 3 of 4 questions to level up!

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