.pf{position:relative;background-color:#fff;overflow:hidden;margin:0;border:0}.pc{position:absolute;border:0;padding:0;margin:0;top:0;left:0;width:100%;height:100%;overflow:hidden;display:block;transform-origin:0 0;-ms-transform-origin:0 0;-webkit-transform-origin:0 0}.bi{position:absolute;border:0;margin:0}.c{position:absolute;border:0;padding:0;margin:0;overflow:hidden;display:block}.t{position:absolute;white-space:pre;font-size:1px;transform-origin:0 100%;-ms-transform-origin:0 100%;-webkit-transform-origin:0 100%;unicode-bidi:bidi-override;-moz-font-feature-settings:"liga" 0}.t:after{content:''}.t:before{content:'';display:inline-block}.t span{position:relative;unicode-bidi:bidi-override}._{display:inline-block;color:transparent;z-index:-1}.pi{display:none}@media screen{.pf{margin:13px auto;box-shadow:1px 1px 3px 1px #333;border-collapse:separate}}.ff1{font-family:ff1;line-height:1.432;font-style:normal;font-weight:400;visibility:visible}.m0{transform:matrix(.322028,0,0,.322028,0,0);-ms-transform:matrix(.322028,0,0,.322028,0,0);-webkit-transform:matrix(.322028,0,0,.322028,0,0)}.v18{vertical-align:-42.352855px}.v16{vertical-align:-40.427725px}.v1c{vertical-align:-31.764641px}.v1b{vertical-align:-28.876946px}.v9{vertical-align:-25.026687px}.v10{vertical-align:-22.138992px}.vf{vertical-align:-18.288733px}.vc{vertical-align:-15.401038px}.v6{vertical-align:-13.475908px}.v7{vertical-align:-10.588214px}.vb{vertical-align:-8.663084px}.vd{vertical-align:-5.775389px}.v2{vertical-align:-3.850260px}.v5{vertical-align:-1.92513px}.v0{vertical-align:0}.v14{vertical-align:1.92513px}.v8{vertical-align:3.850260px}.va{vertical-align:5.775389px}.v12{vertical-align:7.700519px}.v3{vertical-align:9.625649px}.v1a{vertical-align:11.550779px}.v4{vertical-align:13.475908px}.v1{vertical-align:15.401038px}.ve{vertical-align:18.288733px}.v13{vertical-align:20.213863px}.v11{vertical-align:23.101557px}.v1d{vertical-align:25.989252px}.v17{vertical-align:28.876946px}.v19{vertical-align:32.727206px}.v15{vertical-align:45.240549px}.ls1{letter-spacing:0}.ls0{letter-spacing:195.577141px}.sc0{text-shadow:-.015em 0 transparent,0 .015em transparent,.015em 0 transparent,0 -.015em transparent}@media screen and (-webkit-min-device-pixel-ratio:0){.sc0{-webkit-text-stroke:.015em transparent;text-shadow:none}}.ws1{word-spacing:-4.572183px}.ws4{word-spacing:0}.ws3{word-spacing:29.799404px}.ws2{word-spacing:62.855487px}.ws0{word-spacing:107.44831px}._1{width:1.556147px}._6{width:2.671118px}._0{width:3.729939px}._8{width:5.053466px}._3{width:6.503329px}._4{width:7.758674px}._13{width:9.080195px}._2{width:10.720566px}._e{width:13.401711px}._7{width:15.389006px}._5{width:18.112263px}._14{width:21.292737px}._f{width:23.703160px}._d{width:27.505291px}._b{width:30.100206px}._a{width:36.715834px}._12{width:38.743236px}._c{width:49.175033px}._9{width:64.317382px}._11{width:78.834064px}._15{width:142.686206px}._10{width:186.863924px}.fc0{color:transparent}.fs0{font-size:16.042748px}.fs1b{font-size:18.048092px}.fsc{font-size:22.058779px}.fs17{font-size:24.064122px}.fsd{font-size:26.069466px}.fs1f{font-size:30.080153px}.fs9{font-size:32.085496px}.fs20{font-size:34.090840px}.fs2{font-size:36.096183px}.fs13{font-size:38.101527px}.fs4{font-size:40.106870px}.fs14{font-size:42.112214px}.fs1c{font-size:44.117557px}.fs1a{font-size:46.122901px}.fsb{font-size:48.128244px}.fs1d{font-size:50.133588px}.fs5{font-size:52.138931px}.fs12{font-size:54.144275px}.fs10{font-size:56.149618px}.fs1{font-size:58.154962px}.fsa{font-size:60.160305px}.fs11{font-size:62.165649px}.fs6{font-size:64.170992px}.fs8{font-size:66.176336px}.fs3{font-size:68.181679px}.fse{font-size:70.187023px}.fs1e{font-size:72.192366px}.fs22{font-size:74.19771px}.fsf{font-size:76.203053px}.fs7{font-size:78.208397px}.fs19{font-size:80.21374px}.fs18{font-size:82.219084px}.fs21{font-size:84.224427px}.fs16{font-size:86.229771px}.fs24{font-size:88.235114px}.fs23{font-size:90.240458px}.fs15{font-size:104.277862px}.y0{bottom:0}.y2d{bottom:73.996372px}.y2e{bottom:80.195836px}.y2c{bottom:91.974819px}.y2b{bottom:107.473479px}.y2f{bottom:121.422274px}.y2a{bottom:132.58131px}.y29{bottom:174.737667px}.y28{bottom:187.446568px}.y27{bottom:208.83472px}.y16{bottom:242.001854px}.y26{bottom:269.58947px}.y15{bottom:271.759283px}.y25{bottom:299.346899px}.y24{bottom:319.185184px}.y23{bottom:340.263363px}.y22{bottom:344.602988px}.y20{bottom:352.662291px}.y21{bottom:371.570657px}.y1f{bottom:429.535648px}.y1e{bottom:463.012755px}.y1c{bottom:513.538389px}.y12{bottom:518.187987px}.y1{bottom:527.406495px}.y1d{bottom:533.996621px}.y11{bottom:535.546487px}.y1b{bottom:537.406327px}.y1a{bottom:566.543809px}.y19{bottom:586.072121px}.y10{bottom:591.031693px}.yc{bottom:649.61663px}.yd{bottom:656.746014px}.yb{bottom:673.794541px}.yf{bottom:678.444139px}.ye{bottom:698.902371px}.ya{bottom:699.832291px}.y9{bottom:722.460335px}.y8{bottom:757.797282px}.y18{bottom:764.306719px}.y7{bottom:777.325594px}.y14{bottom:779.805380px}.y17{bottom:783.215085px}.y13{bottom:787.864683px}.y6{bottom:826.301362px}.y5{bottom:849.23938px}.y4{bottom:873.41729px}.y3{bottom:890.77579px}.y2{bottom:918.363406px}.h3{height:18.417075px}.h1a{height:20.719209px}.h2a{height:25.323478px}.he{height:27.625612px}.h15{height:29.382293px}.h9{height:41.438418px}.h28{height:48.344821px}.h29{height:51.441072px}.h11{height:55.251224px}.h1d{height:57.553359px}.h12{height:65.045322px}.h4{height:66.761896px}.h1c{height:67.347456px}.h19{height:69.064030px}.h2c{height:70.820711px}.h24{height:72.665627px}.h16{height:74.670971px}.h7{height:75.970433px}.h10{height:77.6469px}.h25{height:82.122827px}.ha{height:82.748494px}.hb{height:83.085392px}.h1b{height:85.259184px}.h20{height:87.481105px}.hc{height:89.783239px}.h21{height:90.577355px}.h2b{height:90.914253px}.h5{height:93.673606px}.h14{height:93.882161px}.hf{height:94.387508px}.h1e{height:94.884833px}.h13{height:99.071990px}.h1f{height:99.826px}.h2e{height:101.293911px}.h17{height:105.096042px}.h8{height:106.146842px}.h2d{height:112.676241px}.h6{height:113.847361px}.h27{height:114.184259px}.h22{height:115.940940px}.h26{height:116.317945px}.h18{height:117.697621px}.hd{height:119.710986px}.h23{height:121.54788px}.h2{height:527.407783px}.h0{height:1054.814278px}.h1{height:1054.964988px}.w1{width:783.817088px}.w0{width:784px}.x0{left:0}.x1a{left:14.144631px}.x1{left:26.54356px}.x3{left:51.961363px}.x4{left:55.061095px}.x1c{left:64.980238px}.x1d{left:67.150051px}.x21{left:70.559756px}.x5{left:98.147372px}.x6{left:102.486997px}.x1f{left:112.716113px}.x1e{left:130.69456px}.x17{left:136.274077px}.x24{left:144.953327px}.x22{left:147.433113px}.xa{left:152.392685px}.x8{left:156.112363px}.x9{left:162.311827px}.x18{left:165.721533px}.x19{left:182.770059px}.x7{left:186.799711px}.x1b{left:223.066577px}.xb{left:236.395425px}.xf{left:278.551783px}.x10{left:286.301113px}.xe{left:288.160952px}.xd{left:289.710818px}.xc{left:296.220256px}.x20{left:311.408943px}.x23{left:345.196023px}.x15{left:394.791738px}.x13{left:408.120586px}.x14{left:409.670452px}.x16{left:425.479086px}.x26{left:492.4333px}.x12{left:520.020916px}.x25{left:527.150300px}.x27{left:534.89963px}.x11{left:555.047889px}.x2{left:709.104576px}

APPM 2360 Lecture 27: Section 8.1 (Continued)

United States

Introduction to Differential Equations with Linear Algebra

Applied Math

Keith Julien

University of Colorado - Boulder

Calculus 3 for Engineers

Weather and the Atmosphere

Theoretical Fluid Mechanics

Mechanics of Materials 1

Calculus 3

Computer Science 1: Starting Computing - Experienced

Principles of Marketing and Management

APPM 2360 Lecture Notes - Lecture 9: File Exchange Protocol

MATH 10041 Chapter Notes - Chapter 2: Fittv

PHYS 4 Chapter Notes - Chapter 33: Chno-Fm

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

All Subjects

Accounting

Mathematics

Statistics

Computer Science

Psychology

Management

Biology

Physics

Chemistry

Electrical Engineering

Mechanical Engineering

Marketing

Music

History

Project Management

Business

Architecture

Geography

Science

Nursing

Information Technology

Engineering

English

Finance

Philosophy

Astronomy

Communications

Sociology

Anthropology

Prealgebra

Algebra

Precalculus

Ethics

Geometry

Probability

Economics