Class Note for MATH 151 at OSU
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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Ohio State University taught by a professor in Fall. Since its upload, it has received 18 views.
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Date Created: 02/06/15
Limits Compute the following limits if they exist CAUTION AVOID AND EFORMS 1 10 11 00 lim 2x 11 Direct substitution Answer 15 rail lim 4 Direct substitution results in the 00 form So factor the denominator xgt72 x cancel x 2 substitute Answer 14 lim xx 2 Answer DNE why xgt27 lim xx 2 Answer 0 rgt2 lim 2 The denominator gets smaller and smaller in this case so the rational xgt27 x expression will get bigger and bigger Also visualize the graph Answer oo x2 11m Answer 00 see 5 H2 x 2 lim The denominator gets bigger in this case so the rational expression will xgtoox get smaller and smaller Also visualize the graph Answer 0 0 to be speci c lim The denominator gets bigger in this case so the rational expression will xgt7oo x get smaller and smaller Also visualize the graph Answer 0 0 to be speci c Caution Eform Divide both the numerator and denominator by x 00 lim xgtoox You will get limi4 Think about it x 2x3 5x2 11 11ml 6x 7 xgt7oo Caution Eform Try dividing both the nr and the dr by x3 00 2 3 Y 3911 t 139 M Oqu ge E l xx3 2 approaches 6whlch approaches 00 5 2 11 11m 3x 2 Caution Eform Try dividing both the numerator and Hi 2x 6x 7 oo denominator by x3 as in the previous problem Observe what happens Did it help Continue Continuity Find the values at which the following functions are discontinuous if any 12 fx EL4 x 13 gx x2 11 14 hx3x 7 15 fxx2 9 2 16 7 f X Ti 16 Find the points at which the following function tx is discontinuous In each case explain the reason Also nd the points at which tx is left continuous and light continuous 17
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