Class Notes

MAC2233 - Calculus for Business and Social Sciences Full Class Notes

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Full class notes for Calculus for Business and Social Sciences (MAC2233). They cover limits, continuity, differentiation rules, marginal cost/revenue/profit, exponential and logarithmic functions, basic integration, and differentiation rules.

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This document introduces the fundamental concept of limits in calculus, explaining how to determine the behavior of a function as it approaches a specific value. Students will learn how to evaluate limits using graphical analysis, understand one-sided limits, and differentiate between a limit and the actual function value at a point.

limits calculus graphical analysis one-sided limits piecewise functions mathematical notation
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Full class notes for Calculus for Business and Social Sciences (MAC2233). They cover limits, continuity, differentiation rules, marginal cost/revenue/profit, exponential and logarithmic functions, basic integration, and differentiation rules.

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SubjectMathematics
CourseMAC2233 - Calculus for Business and Social Sciences Ful...

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LanguageEnglish
SubjectMathematics
Updated OnAug 09, 2026
Number of Pages10
TypeClass Notes
Written2025-2026
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Unit 1 Limit: If f(x) approaches the number L as x approaches (but is not equal to) the number a from both sides of a, then we say that the limit of f(x) as x approaches a is L. It is a y-value that x approaches (but doesn't necessarily touch) as it gets closer to a certain x-value. The notation lim f(x) x -> a is read as "The limit, as x approaches a, of f(x)". lim f(x) x -> a- is read as "The limit, as x approaches a from the left, of f(x)". lim f(x) x -> a+ is read as "The limit, as x approaches a from the right, of f(x)". To find limits using a graph, find the limit from the left and from the right. If they are equal, then that value is the limit. If they are not equal, the limit does not exist. Look at the value the function approaches from each side, not the exact point value if there is one. However to find f(a) of a function, look for the closed point on the graph where x is equal to a. For piecewise functions, plug a into the appropriate function (or both depending on question

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