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test1solution - 501.0110“ 2‘ WKNC SCHEMG Name and...

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Unformatted text preview: 501.0110“! 2‘ WKNC: SCHEMG' Name and student number (print clearly) MATHIOIBA 3.0 Test no. I 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) Q1. (10) a) Consider the function f (x) = 414 — 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) . 0 ts». 2. — L W 4' 5‘ O a) 0.!) L inn. I 4' X, Jana/s t o / i I __ L _ ._ l , “Th-4‘ 01% ad 4 it u r . (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 + M6) [-2 (-3) a) {—4 lim x (8) b) x-¢4_ m (Reminder: [[x]] is the largest integer value not exceeding x.) lim (9) c) tath—‘U4r2+t h ——[——— a; :-~4.‘.,Wu~J-‘t:+ a) 5m“, s’m( ) m micc’lm, 9““ h‘L-Z. , ,, 4:27a- 4,2 : —2__ : 3—: L atmwh‘w L3 Wm. "ML 52»; L; “01*: riffs; W W M “r: W’s la) ii; 34/1 fig; _. i =4“; aw “TV #71;qu 5 <2 Mk“ V \j wast +0 - M (91%}; MM9 «W hggg ( 2x 4 MFA?) ob» inert) u (Malian-l1; C) “L;— CZt—JQtH—t‘)’ Melt—m ) 49—990 air” : ,w w (A#5)0r+'b)='443"3; {2"7r0 M £01.?" Li; + 14th 6 (25) Q3. In this question on are r uired to ive exact values. Sim li as far as possible. or full credit you must give correct reasoning in addition to answers. 212 '3 — (13) a) Evaluate 111(6 0g“ a ),wherea>0 (12) b) Solve forx if 10g4 x =log2 x (25) Q4. x + I . . l' _ a . (1Q 2) Find an equatlon of the tangent me to the/curve y x at a pomt 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] hm x + 1 (10) b) Evaluate the limit 16 .4. 00 x . Use this information to determine the x + 1 horizontal asymptote to the curve y = ——x as It increases without bound. __- " MM W we): Z) 3/1.) TL ”“7””4 W “L“ ( is» 5(3’4'1")“j(’“) i: i 5 . ‘ 2rt+l~ 3 ; M 13:33) : ,1»- m - 2— M4 3C“2.— kw)“; L” : ,2,» 192-; __ J. H") H 2) L62 - Lam Lt 1+1. 7- ‘ . at"; M gm}: HAHN: fie.» J» :__r z. fin 2.0m) 4*— '= was h.2.(1-+|~) a—w 11.112») ‘l ...
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