sn4_1 - Math 2433 Week 4 Popper 004 1. What class is this?...

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Unformatted text preview: Math 2433 Week 4 Popper 004 1. What class is this? a. Math 1325 b. Math 1330 c. Math 1431 d. Math 2433 2. Let 2 3 ln ( ) 3 i j k t t t t e t - = +- h , find 1 ( ) e t dt h a. ( ) ( ) 3 3 3 1 1 2 3 1 i+ j+ k e e e e---- b. ( ) 3 3 3 1 1 2 3 i+ j+ k e e e e--- c. ( ) ( ) 3 3 3 1 1 2 3 1 i+ j+ k e e e e--- + d. ( ) ( ) 3 3 3 1 3 1 i+ k e e e e---- e. ( ) ( ) 3 3 3 1 1 2 3 1 i+ j- k e e e e-- + + 13.4 Arc Length Recall from calc II: (9.8) Arc length and speed: ( ) [ ] ( ) [ ] + = b a dt t y t x c L 2 2 ' ' ) ( ( ) [ ] + = b a dx x f c L 2 ' 1 ) ( ( ) [ ] ( ) [ ] + = d c L 2 2 ' ) ( Speed along a curve: Path ( ) ( ) ( ) t y t x , takes from 0 to t: ( ) [ ] ( ) [ ] + = t du u y u x s 2 2 ' ' So, ( ) ( ) ( ) [ ] ( ) [ ] 2 2 ' ' ' t y t x t s t v + = = Example: Find the arc length of the curve traced out by the parametrics ( ) cos x t a t = and ( ) sin y t a t = over the interval from t = 0 to t = 2 Now apply this to a path C traced out by ( ) x x t = , ( ) y y t = and ( ) z z t = for [ ] , t a b and we have: [ ] [ ] [ ] 2 2 2 ( ) ( ) ( ) ( ) b a L C x t y t z t dt = + + Or ( ) ( ) b a L C r t dt = Examples: Speed: Let r ( t ) = x ( t ) i + y ( t ) j + z ( t ) k , t [ a , b ] be a continuously differentiable curve. If s is the length of the curve from the tip of r ( a ) to the tip of r ( t ), then the speed is: 2 2 2 ds dx dy dz dt dt dt dt = + + Note: a curve is said to be a unit speed curve if ( ) r t is a unit vector for all t Popper 004...
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sn4_1 - Math 2433 Week 4 Popper 004 1. What class is this?...

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