The slope of the normal line to the curve y3 tan2x cos3xy when x 0 is Xo a 3 2

# The slope of the normal line to the curve y3 tan2x

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5. The slope of the normal line to the curve y3 + tan(2x) = cos(3xy) when x = 0 is .. X=o (a) 3 2 (b) 3 2 (c) 2 -3 (d) -2 (e) --3 -2---3 3 556. If lim f(x) ~4 = 5, then lim x f(x) = x-t3 X -x-t3 +b9-Lt == 5 AI \'lY\"~ \'W\ "-3Q~ '..§¥(.. )C~'?, ~~3 "f-l3.
Math 101, Final Exam, Term 131 Page 4 of 14 JMASTERJ 17. If f(x) = 10x2 + 2tanx, then f(3) (x) = '-;f 't<) ~ 20 X -I-~ S~c.. X .I, J. . ;{ seO( ~cx~nX 2 2 2 f('V)::::?-O+':l.(a) sec x(sec x+2tan x) ." _ 20 + s.ec"-x .fc:tnX -'1. L a s..eCK. # (b) 20 sec4 x + 2 sec x tan x tt, S-€('1..X S-R<: x + 'Jl'lt\)( L--tdr '><J., IO.f he} ~ " .s .ec~ 1"" r' (e) sec2 x(sec2 x -tan x) 8. Let H(x) = f(xg(x) -2). If f(4) = 6,1'(4) = -5, g(2) = 3, andg'(2) = -2, then H'(2) = f '(:;r lX) -2) . L'-::i-<J' (-xl 1-~('X)JHI ft.) :; . ~ (a) 5 I [:2cj(2)+:)Cz))H'(2-) -:. f (J.t)cz.J-2-) . (b) -6 := f I ( 4) ~ [a (-1.) + 3. J (c) 10 ';:, _ 5 (-4+?:» - 5 (-I)(d) -15 -) (e) 2
Math 101, Final Exam, Term 131 Page 5 of 14 jMASTERj 9. Using a suitable linear approximation, (1.0002)500 ~ -= It-\00.:'>-;::' =-\~.o ~ x3 + 2x2 -X -2 :I10. Let f(x) = 3 If R is the number of remov-x -x able discontinuities of f and I is the number of infinite discontinuities of f, then ,y....'L (x+1..J _ !X+'Z.) fIX) "" -X (')(L_\)---Q<-f-L) (x1--I)(a) R = 2 and 1=1 --~ "X ()( -I) (b) R = 1 and 1=2 (X+L) (X-I) (xt-I) -=~) (c) R = 0 and 1=3 ~+,'l.. 9'( .~ :!,.I -I (d) R = 3 and 1=0 x \ e6 0 (e) R = 3 and 1=3
Math 101, Final Exam, Term 131 Page 6 of 14 11. If Newton's Method is used to estimate the x-coordinate of the point of intersection of the curves y = sin (x + ;) and y = In(2x + 1) with Xo = 0, then Xl = "T\ f (x):;: \Yl (2-x..-r.f) -SIf\('X+ ~ } pi __ 2. _ CoscX, .....

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