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1. How do you confirm when you have a vertical or a horizontal asymptote

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## 1. How do you confirm when you have a vertical or a horizontal asymptote

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**Thought of the Day**1. How do you confirm when you have a vertical or a horizontal asymptote**Vertical – suspect them at x-values which cause the**denominator of f(x) to be zero. Confirm that the limit as x a is infinite…. Horizontal – suspect rational functions Confirm that as x , y a**What is the definition of LIMIT?**OK…this is like the basis of ALL of Calculus. It was finally “perfected” by Cauchy in 1821. Ready?**Given any if there is a corresponding**such that implies then we say that lim (This is the bare bones important part that you need to memorize…check your text for the detailed version.)**How many different methods are there for evaluating limits?**Can you name several?**Inspection**• Observe graph • Create a table of values • Re-write algebraically • Use L’Hopitals Rule • (only if the form is indeterminate) • 6. Squeeze theorem (rarely used!!)**1.**2. 3. 4. 5. 6. 7. Math Wars!!! Did you know all 7?**lim**= ?**Hole – at x=3 in the example**• Step – usually the function’s description is split up : • Vertical asymptote – at x=1 in the example f(x)={ for x<0 for x>0**If there is a discontinuity at x=a or if there is a sharp**corner at x=a, then the derivative is undefined at x=a**A function that is either always increasing or always**decreasing. (i.e. the derivative is always positive or always negative.)