Math 1140 Test#2

# Math 1140 Test#2 - E 6 Using the(limit definition of...

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Unformatted text preview: E 6. Using the (limit) definition of derivative, show that f(x) : (x — 3)3 is not differentiable at x = 3 . No credit for any other memod. (4 marks) 17‘h October, 2006 Math 1140 - Test#2 (1.5%.4) EMAIL _ _ __. lnstrucﬁgns SM: - 1. Answer each question in the space provided. 2. Show all relevant work for ﬁrll marks. "3 3. Graphical or programmable calculators are not allowed. £/ 4. You have 1hr 35 minutes to complete the exam. Total marks: 50 5. Check that you have 6 pages and 6 questions. 1. Evaluate each limit. If the limit does not exist, show why. Use limit laws where appropri 1__ 2 (a) lim 1 141 1'- x l .1 I !l" (b) lim J49— :2 r4? . 44 + x — 2 (C) 113‘} x » w ((1)1. sin}? J'Rtanzg I 2. (a) State the (limit) definition of the derivative. (1 mark) ( u I (b) Using Ihe (limit) deﬁnition of the derivative, ﬁndf'(x) for f(x) = :2“ . No credit for any other method. (4 maria) (0) Hence or otherwise, ﬁnd the equation of Langent line to the function in (b) at the point (2,112)) (3 marks) I 3.(a)Find rm for 1’ (20:21:34)“; . (4 marks) \J/ (c) Find 3—; fory = (92 Sin(1 + 293). Do not simplify your answer. (4 marks) ((1) Find f'Or) for for) = , and simplify the answer (4 marks) d 4. (:1) Using implicit differentiation ﬁnd 21% at the point (4.1) for yzx — 2x3); = l. (4 marks) (b) Let f (x) = . Find for) and then solve the equation f"(x) I 0. (6 marks) x2+1 5' Find the marginal cost for C(x) = 55,000 + 470x 7 0.25x2 at x = 10 and inlerprer. (4 mark?) ...
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Math 1140 Test#2 - E 6 Using the(limit definition of...

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