A2_Winter2016.pdf - DISTANCE EDUCATION MATH 1500 WINTER...

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DISTANCE EDUCATION MATH 1500 WINTER TERM 2016: D01/D02 Assignment 2 Sections 2.5, 2.6, 2.7, 2.8, 3.1, 3.2. Total Marks: 60 Due Date: Feb 6, 2016 . SHOW ALL WORK to get full marks. Leave answers as exact answers. For example, leave it as 1 7 as opposed to 0.142857. Word problems should be concluded with a sentence and include units. When calculating a derivative, use the definition of derivative ONLY for Q5. 1
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1. [7] Use limits to calculate a and b such that the following function is continuous for all real numbers x. f p x q “ $ & % sin ˆ 3 π 2 x ˙ ` ax ` b x ă ´ 1 3 x “ ´ 1 p a ` b q x 2 ` cos p x ` 1 q x ą ´ 1 2. [4] Show that ln p x ` 2 q “ e 2 x 2 ´ 4 x has a solution on the interval 1 , 0 q . [Note: ln p 2 q « . 6931]. Justify your answer. 3. Evaluate the following limits: (a) [4] lim x Ñ´8 ˆ e x 2 ` 2 ´ x 2 ´ x 3 x 3 ` 7 ˙ . (b) [4] lim x Ñ8 ? 16 x 2 ´ x x ´ 1 . (c) [5] lim x Ñ´8 ` x 3 ` ? x 6 ` x 3 ˘ . 4. [6] Use limits to determine all horizontal and vertical asymptotes for the function y f p x q “ ? 4 x 4 ´ 1 x 2 ` x ´ 6 . 5. [7] Use the definition of the derivative to calculate the derivative of the function
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