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Unformatted text preview: the left size lim− x →2 Therefore, the limit does not exist. f. lim x →1 1 3 x −1 x −1 (x + 1)
x x −1
2 x =1 =0 Hung Nguyen Problem Set 02 Solution GE207C 2.3 Limits Laws/Squeeze Theorem 2.4 Precise Definition of Limit Solution: Let Plot of Graph t = 6 x ⇒ x = t 6 From this new definition t → 1 as x → 1 The given limit can be written as t 2 −1
lim 3 t →1 t − 1
(t − 1)(t + 1) t 2 −1
= lim 3
=
t →1 t − 1
(t − 1) t 2 + t + 1 ( = lim
t →1 2. Show that (t (t + 1)
2 ) + t +1 t =1 = ⎡ྎ
⎛ྎ 2π
lim+ x ⎢ྎ1 + sin 2 ⎜ྎ
x →0
⎝ྎ x
⎣ྏ ) 2 3 when f satisfies the inequalities ⎞ྏ⎤ྏ
⎟ྏ⎥ྏ = 0
⎠ྏ⎦ྏ Using the limit law, we can see that ⎡ྎ
2 ⎛ྎ 2π ⎞ྏ⎤ྏ
lim on 0,1 ⋃(1,2] Solution: Solution: x →0+ 3. Determine...
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This document was uploaded on 02/27/2014 for the course M 408c at University of Texas at Austin.
 Winter '06
 McAdam
 Differential Calculus, Limits

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