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year_1_-_fall_-_calculus_i

year_1_-_fall_-_calculus_i - SOLUTION 2(14.412qu genome...

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Unformatted text preview: SOLUTION 2 (14.412qu genome: Name and student number (print clearly) MATH1013B 3.0 Test no. 1 F2010 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) 01. f _ i (10) a) Consider the function f(x) - 1- 4x2; - E 5 x S 0. Determine its range. (15) b) Work out the inverse of f(x). Determine the domain of f “(10 . How, if at all, is this domain related to the range of fix)? J I v 1- "\ I _+- a O f/4K. ‘ U Es( (3-) CW1 H gm 9; I {Ire-4 01'9")»: ' do (25) 02. 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. [f a limit does not exist, explain why not. lim sin(\lt~4+n!6) t-3 lim (8) b) x_,4' @ (Reminder: [[x]] isthe largest integer value notexeeeding x.) 1. (a) C) {joey—119:2“ I —— - . . - ext-=4 " " K On; WW,M9L*C'%M WW“ ' a) WW S‘V‘L " v _ dflnfmok. who... 3...... m 19-1“ v - 1V) - r " _- QM... EL) 2 St»( 44-1- ‘- “xzpwr WW ’ 'v’m a M. . r .3 M... 1%.... {94 /' CH4) m\_/" M'll“k°§zllg:1}kfs M MS; El: (Vb-(m .\ QMW fizz-3 $.5- M gt +JCHLTC f _ _ ,l H'— Lw" — a 1.,r fl 'Imhofihuuficm Jam t)?!“ 75‘: +J‘ftLrt ' r—t 4:4» gt+thhc @ : ,IJ..——-——-* d:fiM a we amiss-g w L; t ...to be continued... (25) (13) (12) THQMI‘AA/(gv Vc-‘LAvL; a Jule) I ideal : 's 03. In this question, you are required to give exact values. Simplify as far as possible. For full credit you must give correct reasoning in addition to answers. 3 3) Evaluate 111(610g“ a ), where a>0 b) Evaluate [0g3 72- 1083 8 (25) Q4. x — 3 (IO) :1) Find an equation of the tangent line to the curve)’ = x_ 4 at a point on the curve where x=5. [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 — 3 (15) b) Evaluate the limit Use this information to determine the x—3 horizontal asymptote to the curve I" = ——x 4 as it increases without bound. x—roox—4' ...
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