M137.F07.Assign3 - Math 137 ASSIGNlVIENT 3 Fall 2007 Submit...

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Unformatted text preview: Math 137 ASSIGNlVIENT 3 Fall 2007 Submit all boxed problems and all extra problems by 8:20 anm. October 5. All solutions must be clearly stated and fully justified. Use the format, given on UVVACE under Content, in the file Assignment Format for Math 135 and Math 137, TEXT PROBLEMS: Section 1.6— i 18, 598.), (50a), , , 67, 73a) Section 2.2 — 7, E), 11:1, 20: 32 Section 2.3 — 10, , , 25, , 51 Section 2.6 w 11, ill, 3 31, 36, , Appendix D — (:12, 46, , 56, (51, 697 70, , 73 EXTRA PROBLEMS: 133.1 a) Use graphical operations on the basic graphs y = arctan 1r . y : aresinar ; y = fl to sketch graphs of the given functions. (1) = + airctain(2:r] (ii) = éarcsinfiv — 1) (iii) [1(1') 2 b) For the functions and [1(1) in part find g_1(:c) and h‘l(.73) and their domains, and sketch y = g‘lm) and y = h“1(:r) on your graphs in 21) (ii) and er) (iii). 1‘332 n) Find the domain of each function. the range for f and IL. and show that —] S g[.r) g 1 for all ‘1}. Use inequalities which express what you know about the component functions. (1) [(1,7) = e“""”“” — 1 (ii) y(:1;) = 6—3”2 cosx (iii) h(:r;) = arcsiu[c“’) b) Sketch a qualitative graph of [lllNTz See Example l(iii) on pages 25-26 of your Course Notes] E33 a) Use the diagram (right) to find f(:L') = siu(arctan:r). State the domain and range of f. 1)) Use your result. from a) to show that li1nf[3:) = 1 and lim : —L 11—00 Jig—00 (HINT: Recall that: =| :L' i, so for :r < 0, V172 2 —:r.) E34 Find the vertical and horizontal asymptotes of each function a) = 5 '; I c) 12(1) = 6128:; 1333.5 Review the definition of the greatest integer function on page 105 of your text. There a similar function called the least integer function €(r). defined to be the least integer greater than or equal to :17. a) Sketch [(1.7) for —4 S S 4 and explain how it differs from b) A taxi cab charges a. fare consisting of a. flat fee of $5.00 plus $0.50 for each partial or Whole kin. W'rite a function for the fare, where :1; is the distance travelled in km, using whichever of [[;1;]] or is appropriate. c) Sketch a graph of _/'(;r,:) for 0 S :1: S 5 km. and explain whether or not each of the following limits exists: lim (ii) lim.+ f(:z:) ; (iii) lini a 2 1—42,?) 3—» (Lu—:2— E3.()'* The horses on a. Carousel (Merry—go—Round) move up and down verticully according 2 . . . . to Mt) = 0.7sin(§t) + 1; where Mt) in is the height of the horses backs above the platform, and t is time in seconds, as viewed from your location. a.) What is the period of the vertical motion? b) You want to photograph your nephew, who is riding one of the Carousel horses. Your View is partially obstructed by a. safety fence, so you can only take the picture if 1 g h. S 1.5 in. Approximate the first two possible time intervals for this photo. u/LZM/S c) The edge 01‘ the circular platform is moving at 1.2 m/s. 1f the horses go through 5 complete periods vertically during one revolution, What is the radius 7‘ of the Carousel? NOTE: When writing solutions involving limits, it is important to reference any theorems used. Convenient abbreviations are: limit sum rule (LSR); limit precinct rule (LPR); limit quotient rule (LQR); limit composite rule (LCR). ...
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This note was uploaded on 01/25/2010 for the course MATH MATH137 taught by Professor Oancea during the Fall '08 term at Waterloo.

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M137.F07.Assign3 - Math 137 ASSIGNlVIENT 3 Fall 2007 Submit...

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