pracfinFa07sol

pracfinFa07sol - FINAL EXAM MATH 19A 12/11/2007 Instructor:...

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Unformatted text preview: FINAL EXAM MATH 19A 12/11/2007 Instructor: Frank Bauerle, Ph.D. No books, graphing utilities or notes allowed. Show your work. Show your work. Show your work. Your Name: Your TA: Max Your score Problem 1: Problem 2: Problem 3: Problem 4: Problem 5: Problem 6: Problem 7: Problem 8: Problem 9: Problem 10 : Problem 11 (Ee): 30 15 10 10 15 20 20 10 10 20 5 TOTAL: 160 Good Luck and have a great winter break! 1. (30 points) Compute the derivatives dy of the following functions (no need to simplify): dx tan x (a) y = e (b) y = Jsinh(wx) where w is a constant. \ cos k Cw)() W e (c) y = (x 5 - 3x 3 + 12x - 4)(8x - x + 7[2) ( 5 'f-~- 9'(.. L tIL) C g'f -l'-+u,) -\- ({-3/-+lL 'I--lf) -c ~- e)Ce-I) Problem continues on next page ! 1 Problem continued from previous page ! (d) y = In( k 2 + sec 5 + e 2 (37r)) where k is a function that does not depend on x. f(ax + b) (e) y = ( d) where f and 9 are differentiable functions of x, g(x) -=I 0 and a, b, C 9 cx+ and d are constants. (f) y = (sinx)COSX where 0 :::; xl... 7r ~ ~J rA~ t~~ =- COf'{.. ~ l V\ 61 ~ 'I- ) + cos Y- _ ::- ~51 ~ '(-- l \A(?l~ 'f ) \j' ~) 2 2. (15 points) (a) State the Intermediate Value Theorem. I f f~) fj cPLt~ II\u..o UJ 0t1 [a. l ~J ~ (~JA~ \roJw.- 'f slYid-l~ Ioe-~ fC~) CUtd f(k) ~ Ie (X C b C~(0) SO ~~J f(c):=~ (b) Show that sinlr'{z] = x has at least two real solutions. (9R..Q{\J r~O t 5 ~ S\J&. SO\lAJ~(1)'\ . 'L Id fW) ~ S\~"N't)-)( :: (e ~- e-Y-J - y.. ~z.. >- 2..j-I )fL C01(}r~ f(.) If CD~~!I\.LWUJ (J1\ lill rb -tV, ;:;;, y. - 'f. 1t1I~nJ fb Q\A~ 01\ JeAvo..\ 2..e Cifr ~ Z. L ~ r C j) == ( ~. \ ,'2- _ ~ == ct- \) --'- < G -...
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pracfinFa07sol - FINAL EXAM MATH 19A 12/11/2007 Instructor:...

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