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Ernst_Test_2_Fall_2006-1

# Ernst_Test_2_Fall_2006-1 - MATH 101 TEST#2 9‘6 l 10...

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Unformatted text preview: MATH 101 TEST #2 9‘6? l 10 points each NOV. 15, 2006 1. Find the ﬁrst derivative. Use proper notation. e a y=x4e+_4+ edx + 491 x a" . _'._n' 1 f :3/ -"/.' ! rd. Y (K! .J . ‘t ’ “"9 " - L'i L ‘i; "’(e_<’ fﬂef- *1 ~1rA i=4. I I If .- \I 1/u D}! I I? F (I: J. r A " f 1 i: \ <_ I Pl J 6-2.: 0 v (x) = 4; (Use quotient rule and simplify.) 9 +4 I . \_ ’ ‘l_ - I f -; E a.“ “In. \ “FL-7 ,ﬁ \'- ._ 1»? :4; f -. i 9—3 I f U 72¢ d- f (I) = Sin(r2)+sin"(r2)+sinh(r2) " r 3" "" - 1_,{_..-s;. 3 ‘ / H7.” 2. If h(x) = cosh(x), ﬁnd h'(x)then ﬁnd h'(ln3) and simplify using the deﬁnition of sinh(x) and/0r cosh(x). \ L/ ,_—-—'——"'_""' "‘“—-—-._ .‘ — I / J k I?" u I f w. 3' '2 I x I ." tf__,..—--“" _ _ Z _ i I _.;'_ - ' - _ . a F It a J - J "i. I ( / I 7-. -a" i I? . Find the equation of the tangent line to the graph of f(x) = \le + 8 at x =1 . .- _ - + ‘ _ rf - b} ' If 2' {I ’ f .f: - I f . .' I __ " —' | &I . lj , (1 I‘ (J 3 If: z _. r’ ‘, -_"._ .: x r” f' J | {1' j __.-—I , x a 2, ._ J a ‘22 I." / . I «‘3 -"| F x ' I J I; 4. Find the point(s) on the graph of ﬁx) where there is a horizontal tangent line. L f(x) = 111(x2 —2x+2) 5. Find g"( x ). Completely simplify. 10x g(x) = 5+x | ' _. z ‘r .- -/ -. .- I .- .\ .— \ -'. x. =0: n-IC. :. -- fr!)f:':vr)-- }{?kf":l ('1; H J “.r£7‘_|l‘__3"} (JO— re) _’ I” ‘KQP __ ’ f ’ _—___-—F— F P If “5 *>‘ ,=z; Xiarnx' > 93 ;’I/ f. 3; q , * “(my 300,. -. 5‘, :2va M00 — IOX ~93}:— _ . . ,; ______‘d_,_- - ‘) 'I ..'.a-.“"""' ‘0" . ‘I , 13» I i k {hi L" .. a, ’1: - 6. Use implicit differentiation to ﬁnd a: . it");3 = sec(y) _, LA ff'l-n, "1\,\ ——'—" I} K .‘ -— gtc \ a ’3} M. K «f J Jaw” 'P' J ____.._-—-—-'I":" 7. Uk\ r ” -..(- x, mm) M l ( 7. Find f'(x). Sketch both graphs. 'g g I < for) = e ’x'1 lnx , x>l H “x l . L A L { 7'61": r d , A f Q __/' \\ ERR-~— _ _ .__.::< , 4 :L _ ...
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