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Limits Using Algebra

Limits Using Algebra. Objective: to find the limits of functions algebraically using properties of limits. For the next few properties assume. Sum Rule. Example:. Difference Rule. Example:. Product Rule. Example:. Quotient Rule. Example:. Constant Rule. Example:. Power Rule. Example:.

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Limits Using Algebra

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  1. Limits Using Algebra Objective: to find the limits of functions algebraically using properties of limits

  2. For the next few properties assume

  3. Sum Rule Example:

  4. Difference Rule Example:

  5. Product Rule Example:

  6. Quotient Rule Example:

  7. Constant Rule Example:

  8. Power Rule Example:

  9. Sandwich rule • If g(x) < f(x) < h(x) for all x ≠ c in some interval about c and… then

  10. Example of the sandwich rule Solution: Since sin(x) lies between 1 and -1 it follows that And By the sandwich theorem

  11. Lets look at the graph on a calculator • First graph the equation x2sin(1/x) • Hit the window key and set: Xmin=-.1 Xmax=.1 Xscl=1.5 Ymin=-.01 Ymax=.01 Yscl=1 Xres=1 • Now graph x2 and –x2

  12. The sandwich theorem • This theorem is mainly to prove limits that would be difficult to find and are needed to find other more complex limits. • One such limit is • We will explore this proof at a later time.

  13. Example of this in action • Find

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