M137.assign3

M137.assign3 - l\/Iath 137 ASSIGNMENT 3 Fall 2006 Submit...

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Unformatted text preview: l\/Iath 137 ASSIGNMENT 3 Fall 2006 Submit all boxed problems and all extra problems by 8:20 am. October 6. All solutions must be clearly stated and fully justified. TEXT: Section 1.6 — , 64a), 65b), , 69 Section 2.2 — 6, 9, , 14, :17, , 29, 30 Section 2.3 — 2, 10,, 17, , . 41. , 55 Section 2.6 , , 23, 26, 29, , m EXTRAS: 133.1 Usc graphical operations on the basic graphs y = arcsinm and y = arctanzr to sketch the given functions. a) arctan — g b) 2 arcsin (:1: + E32 Evaluate the given expressions, being careful about domains and ranges: —§ 3 arcsin(v) S g for —l S S 1. and —% < arctan(v) < for —00 < < 00. . . 1 . . 57T 37r sm arcsni — b) arcsm sm —1 c) arctan tan T 7T z: , 133.3 a) Find the domain and range of each function; use inequalities which express What you know about the (TOITIPOI'IGI'lt functions. (i) = ez“‘“"““‘" — 1 (ii) g(:l:) = c‘$2 cos :1: (iii) Mr) 2 arcsin(e“’) 1)) Sketch a qualitatch graph of 133.4 a) Use the (liagrzun (right) to find [(17) = sin(arctnnr). State the domain and range of b) Use your result from a) to Show that limflx) = 1 and lim f(:1:) : ,—1. x _ ill—'00 —> oo (HINT: Recall that \/—:r—2 2| :L' l, so for a: < 0‘ VP 2 —2:.) 1333.5 For each of the given functions. use suitable graphical operations to sketch the graphs of y = f(.'r) and y = I/"’(;r,). Find the function f'1(;r) and its domain and range. 111(3: — 1) b) — 2 N .B. W’hen writing solutions involving limits, reference any theorems used. Convenient abbreviatioi‘is are: limit sum rule (LSR.); limit product rule (LPR); limit quotient rule (LQR); limit composite rule (LCR). Maple problem: (Optional: ll suggested by your instructor, submit this problem directly to him/her in Class on October 6. Do not submit to the drop box.) 21) Use Maple to plot the graphs of each function for —37r S a: S 37r. (i) sin(aresin(1:)) (ii) arcsin(sin(m)) b) One of the graphs in a.) is correct and the other is not. By examining the graphs carefully, explaii'i which is which Corrmtent: Computer plotting routines are not infallible! ...
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This note was uploaded on 08/01/2008 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.

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M137.assign3 - l\/Iath 137 ASSIGNMENT 3 Fall 2006 Submit...

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