Math 1140 Test#4

# Math 1140 Test#4 - o 4 Use linear approximation to estimate...

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Unformatted text preview: . o 4. Use linear approximation to estimate ME . (5 marks) 28"” November, 2006 Math 1140 R10- Test#4 (4.1 4 Linear Appr.) Name St.#: Instructions - ﬂ— 1. Answer each question in the space provided. . 2. Show all relevant work for full marks. {L I ?/ 3. Programmable or graphical calculators are not permitted. 4. You have 50 minutes to complete the exam. Total marks: 30 5. Circle your last name and check that you have 4 pages and 4 questions. ln(x2 + 1)“ 4 ’ l. (a) Find f '(x) for f(x) = Twa— (Do not simplify your answer) (3 marks) + e f I i W V 2' I r J l I“ ' “j .J i - . C W I l _I . J i l (b) Find % for x25!" + y = x3 (3 marks) 2 \/ r ’J - j / \ Jf (c) Find y' for y = x“ [Hint! Use logarithmic differentiation} (3 marks) \ My wh‘fZ- M/ﬂ‘ / ‘J 7,7,, r! I ' 5 .i/ ' 2. Given ﬁx): (x—1)e" . f'(x)= (27 we” , f"(.\‘) = (x— 3)e” Sketch the graph of f by ﬁrst ﬁnding: (12 marks) (a) x and y intercepts (b) asymptotes (c) lntcrvals ofincrezise or decrease (d) coordinates ol‘loca] maxima and minima (c) Intervals o! concave up or concave down (1) coordinates ot‘inl‘lcction points [For full marks, clearly labei ail max/min points. inﬂection points, intercepts, and asymptotes 0n the graph] more space on next page... 2. Given f(x): (_x—1)e_'x : f'OC) = (2— X)€-x 9 f“(x) : (x‘ 3)cd Sketch the graph of f by ﬁrst ﬁnding: (12 marks) (a) x and y intercepts (b) asymptotcs (c) Intervals of increase or decrease (d) coordinates oi'locnl mnxima and minima (c) Intervals of concave up or concave down (i) coordinates of inﬂection points [For full marks, clearly label all max/min points, inﬂection points, intercepts, and asymptotes 0n the graph] '1 U” r . r r ‘ t H” .- \3c \' ‘ 3‘. \(L‘ \ i | i / l i \M/ f I \/ \ a , more space on next page... 3, Evaluate each limit ifit exists, using limit laws, rules, and properties. (4 marks) ln(3x + 1) lim (a) 1-00 x ...
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Math 1140 Test#4 - o 4 Use linear approximation to estimate...

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