Worked examples

Limits and continuity

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Limits of ratios of polynomials at a point
• 2Limits by rationalization
• 3Limits at infinity of ratios of polynomials
• 4Fundamental trigonometric limits
• 5Limits with asymptotically equivalent functions
• 6Forms 1 to the power of infinity
• 7Forms infinity minus infinity with roots
• 8Finding asymptotes
• 9Limits with the hierarchy of infinities
• 10Continuity of piecewise-defined functions with a parameter