Limits and continuity Last updated Mar 2, 2020 Page ID2071 Save as PDF ur in 0 12.pg Applications - finding all asymptotes Applications - finding all asymptotes2-6-37f.pg2-6-37g.pg2-6-39.pg2-6-40.pg4-4-33.pg4-4-34.pg4-4-35.pg4-4-36.pg4-4-37.pg4-4-38.pg4-4-39.pg4-4-40.pg4-4-41.pgAPEX 1.6 20.pgAPEX 1.6 22.pgAPEX 1.6 24.pgasymp.pgs2 6 35.pgs2 6 37.pgs2 6 7.pgStewart5 2 6 39.pgStewart5 2 6 40.pgStewart5 2 6 43.pgStewart5 2 6 44.pgur lr 3 3.pgShow allApplications - instantaneous rate of change2-1-05.pg2-1-06.pg2-1-07.pg2-7-20.pg2-7-25.pg2.1.30.pg2.1.7.pg3-3-11.pg3-3-19.pgavgRate.pgavgRate2.pgdi1.pgmel1.pgns2 1 5a.pgns 2 1 5.pgQ17.pgQuestion16ab.pgQuestion17ab.pgrich1.pgrich2.pgs1 1 5.pgs1 1 5 mo.pgs1 6 14.pgs2 1 8a.pgStewart5 2 7 22.pgStewart5 3 3 13.pgStewart5 3 3 16.pgStewart5 3 3 22.pgStewart5 3 3 23.pgStewart5 3 3 24.pgs 2 1 7.pgur lr 6 2.pgShow allApplications - otherc0s5p6.pgQ15.pgQ21.pgStewart5 2 2 10.pgStewart5 2 2 38.pgStewart5 2 3 52.pgStewart5 2 3 60.pgs 2 5 55.pgUR VC 11 12.pgShow allApplications - tangent lines and slopes2-1-04.pg3-3-17.pg3-3-18.pg3-4-49.pg3-4-49a.pg3-4-49b.pg3-4-49c.pgAPEX 2.1 16.pgAPEX 2.1 18.pgc1s1p2.pgQ07.pgQ09.pgs1 1 2.pgs1 1 3.pgs1 2 23.pgs2 1 1a.pgstef2 8p1.pgstef2 8p2.pgStewart5 2 2 34.pgStewart5 2 7 3.pgur dr 1 5 17.pgur dr 1 5 19.pgShow allContinuity - classifying discontinuities2.4.1.pg2.4.17.pg2.4.19.pg2.4.22.pg2.4.24.pg2.4.25.pg2.4.3.pgRemovable 01.pgRemovable 02.pgStewart5 2 5 43.pgStewart5 2 5 6.pgs 2 4 prob01.pgs 2 4 prob02.pgur lr 5 1.pgur lr 5 2.pgur lr 5 3.pgur lr 5 4.pgur lr 5 5 mo.pgShow allContinuity - concept of1210s3p7.pg2-2-12b.pg2-2-12c.pg2-2-12d.pg2-2-12e.pg2-2-12f.pg2-5-11.pg2-5-32.pg2-5-33.pg2-5-34.pg2-5-39.pg2-5-40.pg3-2-71.pg4-1-11.pg4-1-13.pg4-1-15.pg4-1-23.pg4-1-27.pg4-1-28.pg4-1-31.pg4-1-47.pg4-1-53.pg4-1-54.pg4-1-55.pg4-1-56.pg4-1-57.pg4-1-58.pganton1 5 Q18.pganton1 5 Q29.pganton1 5 Q30a.pganton1 5 Q30b.pganton1 5 Q6.pgAnton1 6 Q51.pgAPEX 1.5 11-12.pgAPEX 1.5 16.pgAPEX 1.5 18.pgAPEX 1.5 24.pgAPEX 1.5 26.pgAPEX 1.5 28-29.pgAPEX 1.5 30.pgAPEX 1.5 31.pgc1s5p5.pgc3s1p3.pgc3s1p4.pgc3s1p5.pgEpsilonDelta LimitDNE.pgEpsilonDelta LimitExists.pgGQ Continuity IVT 11.pgGQ Derivatives 01.pgGQ Limits 05.pgns2 2 6.pgp4.pgp5.pgpreview 1 7 b.pgprob1.pgprob3.pgprob5.pgQ17.pgQ19.pgS02.05.Continuity.PTP01.pgs1 5 37.pgs1 5 38.pgs2 5 15.pgs2 5 15 20.pgs2 5 16.pgs2 5 17.pgs2 5 18.pgs2 5 20.pgs2 5 33.pgs2 5 35.pgstef2 5p2.pgstef2 5p3.pgstef2 5p4.pgstef2 5p5.pgstef2 5p6.pgStewart5 2 5 1.pgStewart5 2 5 10.pgStewart5 2 5 11.pgStewart5 2 5 12.pgStewart5 2 5 13.pgStewart5 2 5 14.pgStewart5 2 5 15.pgStewart5 2 5 16.pgStewart5 2 5 17.pgStewart5 2 5 18.pgStewart5 2 5 19.pgStewart5 2 5 2.pgStewart5 2 5 20.pgStewart5 2 5 21.pgStewart5 2 5 22.pgStewart5 2 5 23.pgStewart5 2 5 24.pgStewart5 2 5 25.pgStewart5 2 5 26.pgStewart5 2 5 27.pgStewart5 2 5 28.pgStewart5 2 5 29.pgStewart5 2 5 3.pgStewart5 2 5 30.pgStewart5 2 5 31.pgStewart5 2 5 32.pgStewart5 2 5 33.pgStewart5 2 5 34.pgStewart5 2 5 35.pgStewart5 2 5 36.pgStewart5 2 5 37.pgStewart5 2 5 38.pgStewart5 2 5 39.pgStewart5 2 5 4.pgStewart5 2 5 40.pgStewart5 2 5 5.pgStewart5 2 5 59.pgStewart5 2 5 60.pgStewart5 2 5 61.pgStewart5 2 5 62.pgStewart5 2 5 7.pgStewart5 2 5 8.pgStewart5 2 5 9.pgs 2 4 19.pgs 2 4 22.pgs 2 4 28.pgs 2 4 3.pgs 2 4 30.pgs 2 4 35.pgs 2 4 36.pgs 2 4 prob03.pgur lr 1-5 2.pgur lr 5 1.pgur lr 5 2.pgur lr 5 4.pgur lr 5 6.pgur lr 5 6b.pgur lr 5 7.pgShow allContinuity - intermediate value theorem2.8.17.pgAnton1 6 Q68.pgAPEX 1.5 34.pgAPEX 1.5 35.pgAPEX 1.5 38.pgbis.pgGQ Continuity IVT 10.pgQ11.pgQ13.pgReading Q 02.pgS02.05.IntermediateValueThm.PTP02.pgset11 pr1.pgStewart5 2 5 44.pgStewart5 2 5 45.pgStewart5 2 5 46.pgStewart5 2 5 47.pgStewart5 2 5 48.pgStewart5 2 5 49.pgStewart5 2 5 50.pgStewart5 2 5 51.pgStewart5 2 5 52.pgStewart5 2 5 53.pgStewart5 2 5 54.pgStewart5 2 5 63.pgs 2 4 prob04.pgShow allDefinitions and existence (conceptual)1210s2p29.pg1210s3p9.pg2-4-03.pg2-4-x01.pg2-4-x03.pg2-4-x05.pgAPEX 1.2 5.pgAPEX 1.2 6.pgDelta epsilon definition 1.pgDelta epsilon definition 2.pgEpsilonDeltaLimit.pgEpsilonDeltaLimitLinear.pgLimit-laws-01.pgNumerical 01.pgprob1.pgprob2.pgprob3.pgprob4.pgprob5.pgS02.04.DefineLimit.PTP01.pgs2 R 1-16.pgStewart5 2 2 1.pgStewart5 2 2 3.pgStewart5 2 3 10.pgStewart5 2 3 54.pgStewart5 2 3 55.pgStewart5 2 3 56.pgStewart5 2 3 57.pgStewart5 2 4 3.pgStewart5 2 6 2.pgStewart5 2 6 55.pgStewart5 2 6 56.pgtrueFalse.pgShow allEstimating limits numerically1210s3p12.pg2.1.11.pg2.1.13.pg2.1.15.pg2.1.17.pg2.1.3.pg2.2.1.pg2.2.17.pg2.2.19.pg2.2.21.pg2.2.28.pg2.2.3.pg2.2.30.pg2.2.32.pgAPEX 1.1 12.pgAPEX 1.1 14.pgAPEX 1.1 16.pgAPEX 1.1 18.pgAPEX 1.1 19.pgAPEX 1.1 22.pgAPEX 1.1 6.pgAPEX 1.1 8.pgc1s1p2.pgGQ Limits 07.pgns 2 1 5.pgNumerical 01.pgQ07.pgQ11.pgQ13.pgQ15.pgs1 2 23.pgstef2 1p1.pgStewart5 2 1 1.pgStewart5 2 1 4.pgStewart5 2 1 8.pgStewart5 2 2 13.pgStewart5 2 2 14.pgStewart5 2 2 15.pgStewart5 2 2 16.pgStewart5 2 2 17.pgStewart5 2 2 18.pgStewart5 2 2 19.pgStewart5 2 2 20.pgStewart5 2 2 21.pgStewart5 2 2 22.pgStewart5 2 2 33.pgStewart5 2 2 36.pgStewart5 2 2 40.pgStewart5 3 1 1.pgShow allEvaluating limits - factoring1210s2p21.pg1210s2p22.pg1210s2p26.pg1210s2p27.pg1210s2p28.pg1210s3p3.pg1210s3p4.pg2-3-12.pg2-3-13.pg2-3-14.pg2-3-15.pg2-3-18b.pg2-3-18d.pg2-3-20.pg2.5.37.pg2.5.39.pg2.5.49.pg2.5.53.pg3-2-33.pg3-2-34.pg3-2-43.pg3-2-46.pg3-2-49.pg3-2-50.pg3-2-52.pg3-2-53.pg3-2-54.pg3-2-55.pg3-2-56.pg3-2-59.pg3-2-60.pg3-3-01.pg3-3-02.pgAPEX 1.3 28.pgAPEX 1.3 30.pgLimit 02a.pgLimit 02b.pgLimit 03a.pgLimit 03b.pgLimit 07.pgLimit 09.pgns2 3 18.pgp4.pgprob13.pgprob17.pgprob3.pgprob5.pgprob6.pgpr 10.pgpr 2.pgQ18.pgQ19.pgQ28.pgs1 3 16.pgs1 3 17.pgs1 3 18.pgs1 3 18 mo.pgs1 3 19.pgs1 3 22.pgs1 3 27.pgs1 3 27 mo.pgStewart5 2 3 11.pgStewart5 2 3 12.pgStewart5 2 3 14.pgStewart5 2 3 15.pgStewart5 2 3 17.pgStewart5 2 3 19.pgStewart5 2 3 20.pgStewart5 2 3 21.pgStewart5 2 3 24.pgStewart5 2 3 59.pgs 2 3 14.pgs 2 3 17.pgThomas12-02-04-17.pgur lr 2 7.pgur lr 2 8.pgur lr 2 9.pgShow allEvaluating limits - rationalizing1210s2p23.pg2-3-18c.pg2-3-23.pg2-3-25.pg2.5.21.pg2.5.25.pg2.5.51.pg3-2-57.pg3-2-58.pgLimit 04.pgLimit 08.pgLimit 10.pgprob1.pgprob18.pgStewart5 2 3 23.pgStewart5 2 3 30.pgStewart5 2 3 31.pgStewart5 2 3 58.pgs 2 3 18.pgShow allEvaluating limits - rational expressions2-3-18a.pg2-3-24.pgLimit 05.pgLimit 06.pgs1 3 36.pgStewart5 2 3 28.pgs 2 3 19.pgs 2 3 20.pgur lr 2 14.pgShow allEvaluating limits - trigonometric2.2.24.pg2.5.27.pg2.6.20.pg2.6.21.pg2.6.25.pg2.6.30.pg2.6.34.pg2.6.36.pg2.6.38.pg2.6.40.pg2.6.42.pg2.6.44.pg2.6.46.pg2.6.48.pg2.6.49.pg3-4-37.pg3-4-38.pg3-4-39.pg3-4-42.pg3-4-43.pg3-4-44.pgAnton1 6 Q26.pgAnton1 6 Q28.pgAnton1 6 Q30.pgAnton1 6 Q32.pgAnton1 6 Q36.pgAnton1 6 Q38.pgAnton1 6 Q40.pgAPEX 1.3 23.pgAPEX 1.3 38.pgs2 4 12 mo.pgs2 4 7 mo.pgs2 4 8a.pgStewart5 3 4 38.pgStewart5 3 4 40.pgStewart5 3 4 41.pgStewart5 3 4 46.pgStewart5 3 4 47.pgs 3 3 prob01.pgs 3 3 prob02.pgThomas12-02-04-27.pgThomas12-02-04-29.pgShow allFinding limits using graphs2.2.5.pg3-2-36.pgAPEX 1.4 12.pgAPEX 1.6 12.pggraphLimits.pggraphs.pgpreview 1 2 b.pgpreview 1 2 c.pgpreview 1 7 a.pgpr 5.pgQ01.pgQ03.pgQ05.pgStewart5 2 2 11.pgStewart5 2 2 12.pgStewart5 2 2 37.pgStewart5 2 2 4.pgStewart5 2 2 5.pgStewart5 2 2 6.pgStewart5 2 2 7.pgStewart5 2 2 8.pgStewart5 2 2 9.pgStewart5 2 3 2.pgStewart5 2 6 1.pgStewart5 2 6 10.pgStewart5 2 6 3.pgStewart5 2 6 4.pgStewart5 2 6 9.pgs 2 2 3.pgs 2 2 5.pgs 2 2 6.pgs 2 3 2.pgs 2 5 3.pgs 2 5 4.pgur lr 1-5 1.pgur lr 1-5 1 mo.pgur lr 1-5 3.pgur lr 2 10.pgShow allInfinite limits and vertical asymptotes2-2-21.pg2-2-22.pg2-2-23.pg2-2-23a.pg2-2-24.pg2-2-25.pg2-2-28.pgAPEX 1.6 10.pgAPEX 1.6 16.pgAPEX 1.6 9.pgConditionalQuestion.pgns2 2 xxx.pgprob10.pgprob11.pgprob13.pgprob14.pgprob15.pgprob4.pgprob7.pgprob9.pgstef2 3p2.pgStewart5 2 2 25.pgStewart5 2 2 28.pgStewart5 2 2 29.pgStewart5 2 2 31.pgStewart5 2 2 32.pgStewart5 2 2 39.pgStewart5 2 3 13.pgStewart5 2 3 16.pgStewart5 2 6 34.pgs 2 5 16.pgs 2 5 18.pgur lr 2 6.pgur lr 3 15.pgur lr 3 16 mo.pgur lr 3 17.pgur lr 3 3vert.pgur lr 3 5.pgVertical 01.pgShow allLimits at infinity, horizontal and oblique asymptotes1210s3p6.pg2-6-15a.pg2-6-15b.pg2-6-15c.pg2-6-15d.pg2-6-16a.pg2-6-16d.pg2-6-17.pg2-6-17a.pg2-6-17b.pg2-6-19.pg2-6-21.pg2-6-23.pg2-6-27.pg2-6-43.pg2-6-44.pg2-6-45.pg4-4-23.pg4-4-24.pg4-4-25.pg4-4-26.pg4-4-28.pg4-4-29.pg4-4-31.pg4-4-32.pgAnton1 3 Q10.pgAnton1 3 Q14.pgAnton1 3 Q20.pgAnton1 3 Q22.pgAnton1 3 Q25.pgAnton1 3 Q26.pgAnton1 3 Q30.pgAnton1 3 Q32.pgAnton1 3 Q34.pgAnton1 3 Q36.pgAnton1 3 Q38.pgAnton1 3 Q44.pgAnton1 3 Q48.pgAnton1 3 Q56.pgAnton1 3 Q58.pgAPEX 1.6 11.pgAPEX 1.6 14.pgAPEX 1.6 26.pgAPEX 1.6 28.pgc0s5p2.pgc0s5p6.pgjj10.pgprob1.pgprob10.pgprob12.pgprob14.pgprob2.pgprob3.pgprob4.pgprob5.pgprob6.pgprob8.pgprob9.pgQ12.pgQ13.pgQ14.pgQ26.pgQ31.pgQ33.pgQ41.pgS02.06.LimitsAtInfinity.PTP02.pgS02.06.ObliqueAsymptotes.PTP01.pgS02.06.ObliqueAsymptotes.PTP02.pgs2 6 15.pgs2 6 19.pgs2 6 21.pgs2 6 43.pgs2 6 5.pgs3 5 4a.pgs3 5 4a mo.pgs3 5 5 mo.pgsqueeze2.pgstef2 6p1.pgStewart5 2 6 12.pgStewart5 2 6 13.pgStewart5 2 6 18.pgStewart5 2 6 19.pgStewart5 2 6 21.pgStewart5 2 6 22.pgStewart5 2 6 24.pgStewart5 2 6 25.pgStewart5 2 6 26.pgStewart5 2 6 27.pgStewart5 2 6 28.pgStewart5 2 6 29.pgStewart5 2 6 30.pgStewart5 2 6 31.pgStewart5 2 6 32.pgStewart5 2 6 33.pgStewart5 2 6 35.pgStewart5 2 6 36.pgStewart5 2 6 46.pgStewart5 2 6 48.pgStewart5 2 6 50.pgStewart5 2 6 51.pgStewart5 2 6 52.pgStewart5 2 6 54.pgs 2 5 17.pgs 2 5 26.pgs 2 5 27.pgs 2 5 28.pgs 2 6 16.pgs 2 6 18.pgur lr 3 1.pgur lr 3 10.pgur lr 3 11.pgur lr 3 12.pgur lr 3 13.pgur lr 3 14.pgur lr 3 18.pgur lr 3 18 mo.pgur lr 3 19.pgur lr 3 3horiz.pgur lr 3 4.pgur lr 3 6.pgur lr 3 6 mo.pgur lr 3 7.pgur lr 3 8.pgur lr 3 9.pgShow allMotivational applications (estimation)2.1.1.pgs1 1 2.pgs1 1 4.pgs1 1 5.pgs2 1 1a.pgStewart5 2 1 2.pgStewart5 2 1 3.pgStewart5 2 1 5.pgStewart5 2 1 6.pgStewart5 2 1 7.pgStewart5 2 1 9.pgxs2 1 8.pgShow allOne-sided limits - concept of2-2-12a.pg2-3-40.pg2-3-41.pg2-3-42.pg2-3-44.pg3-2-35.pg3-2-39.pg3-2-72.pg4-1-25.pgAPEX 1.4 13.pgAPEX 1.4 14.pgAPEX 1.4 15.pgAPEX 1.4 18.pgAPEX 1.4 20.pgAPEX 1.4 21.pgns2 2 x.pgns2 2 xx.pgprob12.pgprob13.pgprob16.pgprob4.pgprob8.pgQ21.pgReading Q 04.pgs1 3 48.pgs1 3 48a.pgstef2-3p1.pgstef2 3p3.pgStewart5 2 2 2.pgStewart5 2 3 42.pgStewart5 2 3 43.pgStewart5 2 3 44.pgStewart5 2 3 45.pgStewart5 2 3 46.pgStewart5 2 3 47.pgStewart5 2 3 48.pgStewart5 2 3 49.pgStewart5 2 3 50.pgStewart5 2 3 9.pgs 2 2 7.pgs 2 2 8.pgs 2 3 34.pgs 2 5 20.pgShow allRules of limits - basic1210s3p2.pg2-3-03.pg2-3-03a.pg2-3-06.pg2-3-07a.pg2-3-07b.pg2-3-08.pg2-3-09.pg2-3-37.pg2-5-31.pg2.2.7.pg2.3.1.pg2.3.16.pg2.3.19.pg2.3.27.pg2.3.29.pg2.3.7.pg2.4.71.pg2.4.77.pg2.4.79.pg2.5.47.pg3-2-13.pg3-2-14.pg3-2-15.pg3-2-17.pg3-2-18.pg3-2-20.pg3-2-21.pg3-2-22.pg3-2-25.pg3-2-26.pg3-2-29.pg3-2-30.pg3-2-30a.pg3-2-31.pg3-2-41.pg3-2-45.pg3-2-51.pgAnton 1 2 Q34.pgAnton 1 2 Q36.pgAPEX 1.3 16.pgAPEX 1.3 19.pgAPEX 1.3 21.pgAPEX 1.3 22.pgAPEX 1.3 26.pgAPEX 1.3 6-13.pgAPEX 1.3 8.pgGQ Limits 10.pgGQ Limits 11.pgGQ Limits 12.pgGQ Limits 13.pgGQ Limits 16.pgGQ Limits 17.pgLimit 01.pgns 2 3 1 mo.pgns 2 3 3-7.pgprob1.pgprob2.pgReading Q 04.pgs1 3 12.pgs1 3 17.pgs1 3 3 mo.pgs1 3 4.pgs1 3 5.pgs1 3 6.pgstef2 5p1.pgStewart5 2 2 35.pgStewart5 2 3 1.pgStewart5 2 3 3.pgStewart5 2 3 4.pgStewart5 2 3 5.pgStewart5 2 3 51.pgStewart5 2 3 53.pgStewart5 2 3 6.pgStewart5 2 3 7.pgs 2 3 1.pgs 2 3 12.pgs 2 3 4.pgThomas12-02-04-11.pgThomas12-02-04-15.pgTrig-limit-01.pgTrig-limit-02.pgTrig-limit-03.pgur lr 2 10b.pgShow allSqueeze theorem2.6.12.pg2.6.2.pg2.6.7.pgAPEX 1.3 34.pgAPEX 1.3 36.pgGQ Limits 14.pgsqueeze.pgStewart5 2 3 33.pgStewart5 2 3 34.pgStewart5 2 3 35.pgStewart5 2 3 36.pgStewart5 2 3 37.pgStewart5 2 3 38.pgStewart5 2 6 49.pgStewart5 2 6 53.pgs 2 3 30.pgs 2 5 33.pgur lr 2 11.pgur lr 2 11 mo.pgShow all