1. Calculus I (MAT 145) Dr. Day Wednesday January 23, 2019
Approachment  Limits!
Techniques for Determining the Value of a Limit
Numerical Approximation: Same process we used last week
Graphical Approximation: Visual determination
Algebraic Representation: Determining an exact value!
Quiz #2 today
Friday: Quiz #3
Friday, Feb 1: Test #1 in STV 346

2. Approachment
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3. The concept of LIMIT!
This says that the values of f(x) tend to get closer and closer to the number L as x gets closer and closer to the number a (from either side of a) regardless of the value of f(a).
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4. “The limit of f(x), as x approaches a, is L.”
The concept of LIMIT!
“The limit of f(x),
as x approaches a,
is L.”
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6. What happens when you evaluate f(t) at t = 0?
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7. Friday, January 18, 2019
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8. t
f(t)
-0.5
-0.1
-0.01
-0.001
?????
0.0001
0.001
0.01
0.1
0.5
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11. lim 𝑥→1 𝑓(𝑥 Numerical Approachment? Graphical Approachment? Directly?
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12. Friday, January 18, 2019
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13. lim 𝑥→1 𝑓(𝑥 Numerical Approachment? Graphical Approachment?
Direct Calculation?
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14. Write 3 limit statements for this situation.
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15. the function exists at a.
When limit exists
If and , then
If the left-hand limit exists and the right-hand limit exists and they are the same value, then the overall (two-sided) limit exists.
Limits can exist
whether or not
the function exists at a.
And, if the function does exist, but is not the same value as the limit at a (i.e., f(a)≠L), that’s okay, and, in fact, that’s how we know that a function is discontinuous at x=a (stay tuned: Section 2.6).
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17. Evaluate each limit, if it exists, based on the graph of g(x).
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19. Vertical Asymptotes
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20. Limits and Vertical Asymptotes
Use limit statements to describe the vertical asymptotes.
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21. LIMIT LAWS! Suppose that c is a constant and the limits and exist.
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22. MORE LIMIT LAWS!
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23. Friday, January 18, 2019
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24. Friday, January 18, 2019
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25. What happens when you evaluate f(t) at t = 0?
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26. Friday, January 18, 2019
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27. t
f(t)
-0.5
-0.1
-0.01
-0.001
?????
0.0001
0.001
0.01
0.1
0.5
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28. Friday, January 18, 2019
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29. of the curve y = f(x) if either:
The line y = L is called a
horizontal asymptote
of the curve y = f(x) if either:
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33. Friday, January 18, 2019
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34. by finding its intercepts and its limits as and as .
Sketch the graph of
by finding its intercepts and its limits
as and as .
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