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Pre-Calc Homework Solutions 411

# Pre-Calc Homework Solutions 411 - Section 10.3 22 v(t...

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13. 1 E sec t tan t dt 2 i 1 1 E tan t dt 2 j 5 (sec t 1 C 1 ) i 1 (ln ) sec t ) 1 C 2 ) j 5 (sec t ) i 1 (ln ) sec t ) ) j 1 C 14. 1 E } 1 t } dt 2 i 1 1 E } 5 2 1 t } dt 2 j 5 (ln ) t ) 1 C 1 ) i 1 ( 2 ln ) 5 2 t ) 1 C 2 ) j 5 (ln ) t ) ) i 2 (ln ) 5 2 t ) ) j 1 C 15. r ( t ) 5 ( t 1 1) 3/2 i 2 e 2 t j 1 C , and r (0) 5 i 2 j 1 C 5 0 , so C 5 2 ( i 2 j ) 5 2 i 1 j r ( t ) 5 (( t 1 1) 3/2 2 1) i 2 ( e 2 t 2 1) j 16. r ( t ) 5 1 } t 4 4 } 1 2 t 2 2 i 1 1 } t 2 2 } 2 j 1 C , and r (0) 5 C 5 i 1 j , so r ( t ) 5 1 } t 4 4 } 1 2 t 2 1 1 2 i 1 1 } t 2 2 } 1 1 2 j . 17. } d d r t } 5 ( 2 32 t ) j 1 C 1 and r ( t ) 5 ( 2 16 t 2 ) j 1 C 1 t 1 C 2 . r (0) 5 C 2 5 100 i , and } d d r t } ) t 5 0 5 C 1 5 8 i 1 8 j . So r ( t ) 5 ( 2 16 t 2 ) j 1 (8 i 1 8 j ) t 1 100 i 5 (8 t 1 100) i 1 ( 2 16 t 2 1 8 t ) j . 18. } d d r t } 5 2 t i 2 t j 1 C 1 , and r ( t ) 5 1 2 } t 2 2 } 2 i 1 1 2 } t 2 2 } 2 j 1 C 1 t 1 C 2 r (0) 5 C 2 5 10 i 1 10 j , and } d d r t } ) t 5 0 5 C 1 5 0 , so r ( t ) 5 1 2 } t 2 2 } 2 i 1 1 2 } t 2 2 } 2 j 1 (10 i 1 10 j ) 5 1 2 } t 2 2 } 1 10 2 i 1 1 2 } t 2 2 } 1 10 2 j 19. v ( t ) 5 (1 2 cos t ) i 1 (sin t ) j and a ( t ) 5 (sin t ) i 1 (cos t ) j . Solve v ?
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