Functions and Continuity
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Combining limits
Equations are omitted for technical reasons - download the original pdf
We can combine limits in much the same way that we combine numbers. Scalar multiple of a limit Multiplying a function by a constant has the effect of multiplying the corresponding limit by the same constant. In symbols, let a be a real number, then [Equation goes here - download the original pdf to see it.] Alternative notation [Equation goes here - download the original pdf to see it.] Sum of limits The limit of a sum (or difference) of two limits is the sum (or difference) of the limits. [Equation goes here - download the original pdf to see it.] Alternative notation [Equation goes here - download the original pdf to see it.] Product of limits The limit of a product is the product of the limits. [Equation goes here - download the original pdf to see it.] Alternative notation [Equation goes here - download the original pdf to see it.] Quotient of limits The limit of a quotient is the quotient of the limits.[Equation goes here - download the original pdf to see it.] Alternative notation [Equation goes here - download the original pdf to see it.] Example (7) Evaluate [Example goes here - download the original pdf to see it.]
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Contents of
Functions and Continuity
1 Functions
2 Graph
3 Inverse of a Function: monotone increasing or decreasing functions
4 The reciprocal function - singularities
5 Functions defined piecewise on their domain
6 Limits
7 Formal definition of a limit
8 Formal definition of the limit of a function at a point x = a
9 Informal arguments
10 Continuity
11 Combining limits
12 Quotients
13 Image set
14 Inverse image
15 Odd and even functions
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