Unformatted text preview: MA’I‘H 137 FINAL EXAMINATION INFORMATION FALL 2007 1. The ﬁnal examination in MATH 137 will be held TUESDAY, DECEMBER 11th, 4:006:30 p.111. in the
PAC (Sections 112), RCH 103, 105 (Section 13), and RCH 110, 105 (Section 14).
2. Tutorial assistance will be available in the Tutorial Centre1 MC 4067 on December 9th (1—7 pm). 10th (10 ant7 pm), and December 11th (10 a.1n.2 pm). In addition, a Question/Answer session will be held Tuesday December 11th. 12—2 pm, in DC 1350. Otherwise, see your instructor. 3. A sample exam can be found under iSample Exam for Math 137’ on this website. The Math Society also has previous exams from which some problems are useful. 4. Your ﬁnal exam is structured as follows: 0 The ﬁrst two problems deal with basic concepts (ﬁnding limits. derivatives, antiderivatives, deﬁnite inte—
grals) ~ 3035 straigl'iti‘oi'ward marks. Suggestion: work through the ‘Reviews’ of Derivatives and Inte—
grals, in the Content/Final Exam folder on UVVACE, and review the graphs and properties of all basic
functions: (1:70 for )3 any integer and p = 1/2. 1/3. 2/3, cm, in 3:, sin IL‘, cos L tan :r, sec 1‘, arcsinm. arctan a") o The next four problems deal with applications of these basic concepts (curve sketching. related rates,
optimizatiom area, net change from a given rate, linear approximation, Newton’s method) ~ (10 marks. 0 The last two problems are mainly theoretical‘ involving statements and proofs of theorems, as well as
applying them to short answer questions (~ 25 marks). Here is a list of theory you need to know to do the exam problems successfully: 1. All definitions used in the course. 2. Statements (in full) of the following theorems, and proofs of those marked *: — the Squeeze Theorem (Text — page 105) ' 0
$111 : 1 — the basic trigonometric limit: 51—13%) 9  the Intermediate Value Theorem (Text — page 126) — L’Hopital’s Rule (Text — page 299) * The Inverse Function Derivative Theorem (Course Notes  page 50) — The lilxtreme Value Theorem (rl‘ext — page 272) * Fermat's Theorem (Text — page 273) * The Increasing linnctiou Theorem (Text — page 287) — the Mean Value Theorem (Text — page 282) * Theorem 4 (dill'erentiability => continuity) (Text — page 158)  The Fundamental Theorems of Calculus (Text — pages 381 and 384) — The Net Change Theorem (Text — page 394)
In addition, you need to know how to illustrate (geometrically) simple Riemann sums Rn, Ln and All” (as
in Figure 1f Text page 496) and the T rapezoidal Rule (as in Figure 2, Text page 497), how to develop the
integral representing the area between two curves (as in Example 1, Text page 416), and the geometry
behind Newton’s Method as well as the iterative scheme. (Text — page 335). The exam will NO'l' cover the Bisection method, nor Simpson’s Rule. 5. Your final grade will be calculated as follows: the 2 Maple Labs and the best 8 of your 9 assignments (10%), plus your 2 tests (30%), plus your ﬁnal exam (60%) equals your final grade (100%). ...
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 Fall '08
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