FM5002-HW5-2.22.12

# On the other hand 2h 46 46 2h 2h 46 2 the limit exists

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Unformatted text preview: mpute 4 z z. 2 d . Show that the complexlimit 32 h4 32 lim h0 h 54 a. does n ot exist . 1 4 z 4 z 5 2 2 2 t5 4 2 1 5 2 4 1 29 t 2 2 t 8t 5 2 16 0 4 b. 1 z 1 4 5 54 464 t 3 841 t 4 3444 t 3158 t 2 t 6463 12 926 3 15 4 t 1 4 4 . t 0 1 1 4 41 1 17 t 2 2 t 42 t 1 4 1681 0 4 c. 296 t 2 64 t 0 4 z 1428 t 3 289 t 4 t 0 1 4 z z 4 2 2 2 t4 4 2 10 687 42 748 15 15 t 0 1 4 2 4 20 t 2 2 t 8t 1 4 2 16 0 54 z 4 z 4 z 21 628 3 2 h0 0042− 3. 4 h h0 3 3 4 2 lim 4 h h 3 2 4 lim h0 320 t 3 400 t 4 t 704 352 3 3 15 156 h 62 h 2 h0 h 2 224 t 2 29 822 15 z 54 d . lim 64 t 0 4 2 lim t 0 104 h 12 h 3 h4 h 42 h 2 h 8 h3 h4 156. On the other han d, 104 . Therefore, the limit does n ot exist . . FM5002−HW5−2.22.12.nb Let P = p (x, y) = −y. Let Q = q (x, y) = x. 2 Let V: 2 be the vector field defin ed by V x, y P, Q . Let Α (t) = (5, 3 + t), Β (t) = (5 − 3t, 4), Γ (t) = (2, 4 − t), ∆ (t) = (2 +3 t, 3), for 0 &lt;= t &lt;= 1. Compute 1 1 VΑ t Α’ t 1 V Βt t 0 Β’ t 0 1 Α’ t 0 Β’ t 0, 1 t 3 t, 4 3, 0 t 1 1 0 0 3t 0 1 12 t t 0, 1 3, 0 t t, 2 0, 1 t 0 1 2t 0 9t 6. 0 Let Α (t) = (5, 3 + t), Β (t) = (5 − 3t, 4), Γ (t) = (2, 4 − t), ∆...
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