13112an2.5-6

# 13112an2.5-6 - c Kendra Kilmer Section 2.2 The Limit of a...

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Unformatted text preview: c Kendra Kilmer January 11, 2012 Section 2.2 - The Limit of a Function Deﬁnitions: Left-Hand Limit: We write lim f (x) = K if f (x) is close to K whenever x is close to, but to the left of c. x→c− Right-Hand Limit: We write lim f (x) = L if f (x) is close to L whenever x is close to, but to the right of c. x→c+ (Two-Sided) Limit: We write lim f (x) = M if the functional value f (x) is close to M whenever x is close, but not x→c equal, to c (on either side of c). Note: For a (two-sided) limit to exist, the limit from the left and the limit from the right must be equal. That is Example 1: Use the graph below to ﬁnd the following limits: 6 5 4 3 f(x) 2 1 −6 −5 −4 −3 −2 −1 a) b) 123 −1 −2 −3 −4 −5 −6 lim f (x) f) lim f (x) lim f (x) g) lim f (x) x→−3− x→−3+ x→1 x→4− c) lim f (x) h) lim f (x) d) lim f (x) i) lim f (x) x→−3 x→1− x→4+ x→4 e) lim f (x) x→1+ 5 4 56 c Kendra Kilmer January 11, 2012 Example 2: Sketch the graph of an example of a function f that satisﬁes all of the given conditions. • lim f (x) = 1 x→0 • lim f (x) = −2 x→3− • lim f (x) = 2 x→3+ • f (0) = −1, f (3) = 1 tan 3x . Conﬁrm your result graphically. x→0 tan 5x Example 3: Use a table of values to estimate lim x2 + x √ Example 4: Use a table of values to estimate lim . Conﬁrm your result graphically. x→0 x3 + x2 Section 2.2 Highly Suggested Homework Problems: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 6 ...
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13112an2.5-6 - c Kendra Kilmer Section 2.2 The Limit of a...

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