MATH
SK-Laplace Final Problems

# SK-Laplace Final Problems - 1 I 2 3 tut rr 1 s I i lc...

• Notes
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/ tut rr s) 1. I 2. e'' 1 t s s>0 s-a nt. ----'-:. sfl+r: r(p + 1) ----Ili- ' s,'' a s2 + a2' s s2 + a2' a ^2 ^2' J -U .s ) ), J -Cl b I .1' (s-a)-*b- s-a (s-a)2+b2' nt lc I i: Ift^t1 ''l i f' r"1 r ;q \3. )' \t'."\, !i i a rt I !. :*' "\ 4 1 I 1 I I I. I I L IE, Lis s>a s>0 3. tn: n - positive integer 4.to , p 5. sin ar 6. cos at 7. sinhat > -l 8. coshar 9. eo' sin br 10. e^t cos br ll. t"eot , n - positive inte-ger s>0 s>0 s>0 s>lal s>lal l:* t w, ( I'L) !*, (..o l/nrp,.l %*--^_ | ( t'.:. 11 b,i I rL ') rf", I n - - 1* i'iij i: 1'-{ll il t l*{5/. LL-r" *'+d, -"')r ' .i ; \i.l tl jt ^ o-cs I i,! i L - *tt' ' ar'l I \ tL. .l . D\L-g:' : tl**l s>a .t>d >a 7-r> n 1, r '-'l l'tri i t **i L2. u,(t) 13. u,.(t) f (r - c) 11. e''' f (t) (s - a;'+t ' - /'( e'- *-r S s e-.' F(s) F(s - c) 1r /:) c \c/' F (s) G (s) e-r't >0 .rA- (E'+L- ) 2l , b 9i'" \!'u ) zV' s 15. /(cr) 16.Jo fQ-r)s(t)dt 17. 6(r - c) 18. /(")1r; 19. (-r)"/(r) c>0 l- qp\e La- -E.L\e- t-r"d ^\ t &J 'n ''h- l' h..Ua U^*+ 13 d \' I Wt',,t\$O"L\\t'+|')-

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. Lop {o,* e tht F''^ai F"0t og b- c I tri:i gz +!g+ _kf" pLt" coo bs So S'+iig +g:_ t f, 3 .u' olt lq I ,t lro I lz L I ic r l 1 t I L q/l K_ c ( O tr.1r. J- rt ' ./* c_ --_l )J s + Z )u u* | 5- F\g)-* g- 3 l (sr . ).-r \ ),-^-.ralt eL,il err q -5 l [sar r.+ to i Q-r- r %*+ I r,', r t , r jr'- J { I A= tl (,"= ' !c -t- 1 A '1',{ L 'l rl \ v- t^:ar-t ^zt I Co!
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• Winter '09
• SidneyTrudeau

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