test1solution - SOLUTloN é Middlqu Emma" Name and...

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Unformatted text preview: SOLUTloN é Middlqu Emma" Name and student number (print clearly) MATH1013A 3.0 Test no. 1 F2011 Time: 45 minutes Value: 100 No calculators or written material allowed. Attempt as many questions as you please. Maximum is 100. Marks are indicated for each question or part thereof. Part marks will be awarded for relevant and correct intermediate work. Do not hand in additional sheets. If you write overleaf, material will be ignored unless you clearly indicate that this material should be taken into consideration. (Marks) (25) Ql. (10) a) Consider the function f(x) = 44 — x2; 0 s x s 2. Determine its range. ( 15) b) Work out the inverse of f(x). Determine the domain and range of f '1 (x) . CL) P O 5.2.! 4-.)0" ‘5’- & 0/ 3.0%— ml. _' h l t 0/ _L':E.EO .. _. ya a. “as. H» ‘iwmwe .1 W ,1 P‘VIMM ______________r_a (25) Q2. In this question, do not use a table of values to suggest a limit. Use appropriate laws or rules to evaluate the following limits if they exist, explaining your reasoning as you proceed. Correct answer without valid reasoning will not receive full merit. If a limit does not exist, explain why not. lim sinNt - 4 + m’6) t-2 (8) a) t—>4 lirn x (8) b) xfl4_ m (Reminder: [[XJ] is the largest integer value not exceeding x.) lim (9) C) 23—114? +t‘ t ~—1 oo 4cma 4H2 : 2. r T r w MW“ dwwwi‘w Us Wm- fob? _ W” W l3 M L: wax/“1 “9. WW. WWimsz ) 1L4“?- XII f- jiri—flfl“ I I W 0.44M Mom was 5 C93 (147* JirtLr-t) We . p» megabit?“ "fi’o it + 144%» I: Mk.“ ‘ Jt rill/25 (25) Q3. " 21 3 I (13) :1) Evaluate 111(6 0g“ a ) , where a>0 (12) b) Solve for X if 1034 x = log x (25) Q4. x+1 (IQ 3) Find an equation of the tangent line to the curve .‘I' = '_—x at a point on the curve where x=2. [Note: you must use obtain the derivative as a limit. Using the “quotient rule” as per Ch.3 will merit little credit. Hint: work out the coordinates of the point on the curve where the tangent touches the curve, figure out the slope of the tangent line, and use the point-slope formula] lim x+l (10) b) Evaluate the limit . Use this information to determine the I “9' 00 .X x+l horizontal asymptote to the curve )’ = ‘x— as it increases without bound. 2+ I a.) a/t" 1.51,, j; T : "/1 - MW WMm(afl/L) £51 # m : M vol-PIA) M ‘76") s «n "6 . r J c __ .ZHrl/v __ .2 M u”) 1 #- .Jn _:%___ M'?‘ acwz. b6” LL xa-I. _ 3 ; 2”“ “To” 7. - i Mi“) _ :2) L—a‘.’ ————-—-—— ' LA-Do a 2+1. 7— 1cm; {A} ' -Lu. _ i \ M -3(2J? _— . :- 2F : ’6'” lCX—l-l) "37" = Elk-wt: la- l.(l+l~} LL40 Laft‘) ...
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This note was uploaded on 11/05/2011 for the course CHEM 1500 taught by Professor Hameedmmirza during the Spring '11 term at York University.

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test1solution - SOLUTloN é Middlqu Emma" Name and...

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