{"id":150,"date":"2026-01-12T15:55:19","date_gmt":"2026-01-12T15:55:19","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&#038;p=150"},"modified":"2026-01-12T15:55:19","modified_gmt":"2026-01-12T15:55:19","slug":"understanding-limits-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/understanding-limits-get-stronger-answer-key\/","title":{"raw":"Understanding Limits: Get Stronger Answer Key","rendered":"Understanding Limits: Get Stronger Answer Key"},"content":{"raw":"<h2 class=\"entry-title\">A Preview of Calculus<\/h2>\r\n<p id=\"fs-id1170573593926\">For the following exercises (1-3), points [latex]P(1,2)[\/latex] and [latex]Q(x,y)[\/latex] are on the graph of the function [latex]f(x)=x^2+1[\/latex].<\/p>\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]2.2100000[\/latex]<\/li>\r\n \t<li>[latex]2.0201000[\/latex]<\/li>\r\n \t<li>[latex]2.0020010[\/latex]<\/li>\r\n \t<li>[latex]2.0002000[\/latex]<\/li>\r\n \t<li>[latex](1.1000000, 2.2100000)[\/latex]<\/li>\r\n \t<li>[latex](1.0100000, 2.0201000)[\/latex]<\/li>\r\n \t<li>[latex](1.0010000, 2.0020010)[\/latex]<\/li>\r\n \t<li>[latex](1.0001000, 2.0002000)[\/latex]<\/li>\r\n \t<li>[latex]2.1000000[\/latex]<\/li>\r\n \t<li>[latex]2.0100000[\/latex]<\/li>\r\n \t<li>[latex]2.0010000[\/latex]<\/li>\r\n \t<li>[latex]2.0001000[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]y=2x[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]3[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]2.0248457[\/latex]<\/li>\r\n \t<li>[latex]2.0024984[\/latex]<\/li>\r\n \t<li>[latex]2.0002500[\/latex]<\/li>\r\n \t<li>[latex]2.0000250[\/latex]<\/li>\r\n \t<li>[latex](4.1000000,2.0248457)[\/latex]<\/li>\r\n \t<li>[latex](4.0100000,2.0024984)[\/latex]<\/li>\r\n \t<li>[latex](4.0010000,2.0002500)[\/latex]<\/li>\r\n \t<li>[latex](4.00010000,2.0000250)[\/latex]<\/li>\r\n \t<li>[latex]0.24845673[\/latex]<\/li>\r\n \t<li>[latex]0.24984395[\/latex]<\/li>\r\n \t<li>[latex]0.24998438[\/latex]<\/li>\r\n \t<li>[latex]0.24999844[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]y=\\frac{x}{4}+1[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]\\pi[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\u22120.95238095[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99009901[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99502488[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99900100[\/latex]<\/li>\r\n \t<li>[latex](\u22121;.0500000,\u22120;.95238095)[\/latex]<\/li>\r\n \t<li>[latex](\u22121;.0100000,\u22120;.9909901)[\/latex]<\/li>\r\n \t<li>[latex](\u22121;.0050000,\u22120;.99502488)[\/latex]<\/li>\r\n \t<li>[latex](1.0010000,\u22120;.99900100)[\/latex]<\/li>\r\n \t<li>[latex]-0.95238095[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99009901[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99502488[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99900100\u00a0[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]y=\u2212x-2[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]\u221249[\/latex] m\/sec (velocity of the ball is [latex]49[\/latex] m\/sec downward)<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]5.2[\/latex] m\/sec<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]-9.8[\/latex] m\/sec<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]6[\/latex] m\/sec<\/li>\r\n \t<li><\/li>\r\n \t<li>Under, [latex]1[\/latex] unit<sup>2<\/sup>; over: [latex]4[\/latex] unit<sup>2<\/sup>. The exact area of the two triangles is [latex]\\frac{1}{2}(1)(1)+\\frac{1}{2}(2)(2)=2.5 \\text{ units}^2[\/latex].<\/li>\r\n \t<li><\/li>\r\n \t<li>Under, [latex]0.96[\/latex] unit<sup>2<\/sup>; over, [latex]1.92[\/latex] unit<sup>2<\/sup>. The exact area of the semicircle with radius [latex]1[\/latex] is [latex]\\frac{\\pi (1)^2}{2}=\\frac{\\pi }{2}[\/latex] unit<sup>2<\/sup>.<\/li>\r\n \t<li><\/li>\r\n \t<li>Approximately [latex]1.3333333[\/latex] unit<sup>2<\/sup><\/li>\r\n<\/ol>\r\n<h2>Introduction to the limit of a function<\/h2>\r\n<p id=\"fs-id1170572347378\"><strong>In the following exercises (1-3), set up a table of values to find the indicated limit. Round to eight digits.<\/strong><\/p>\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\u22120.80000000[\/latex]<\/li>\r\n \t<li>[latex]\u22120.98000000[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99800000[\/latex]<\/li>\r\n \t<li>[latex]\u22120.99980000[\/latex]<\/li>\r\n \t<li>[latex]\u22121.2000000[\/latex]<\/li>\r\n \t<li>[latex]\u22121.0200000[\/latex]<\/li>\r\n \t<li>[latex]\u22121.0020000[\/latex]<\/li>\r\n \t<li>[latex]\u22121.0002000;[\/latex]<\/li>\r\n<\/ol>\r\n[latex]\\underset{x\\to 1}{\\lim}(1-2x)=-1[\/latex]<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\u221237.931934[\/latex]<\/li>\r\n \t<li>[latex]\u22123377.9264[\/latex]<\/li>\r\n \t<li>[latex]\u2212333,777.93[\/latex]<\/li>\r\n \t<li>[latex]\u221233,337,778[\/latex]<\/li>\r\n \t<li>[latex]\u221229.032258[\/latex]<\/li>\r\n \t<li>[latex]\u22123289.0365[\/latex]<\/li>\r\n \t<li>[latex]\u2212332,889.04[\/latex]<\/li>\r\n \t<li>[latex]\u221233,328,889[\/latex]<\/li>\r\n<\/ol>\r\n[latex]\\underset{x\\to 0}{\\lim}\\frac{z-1}{z^2(z+3)}=\u2212\\infty [\/latex]<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]0.13495277[\/latex]<\/li>\r\n \t<li>[latex]0.12594300[\/latex]<\/li>\r\n \t<li>[latex]0.12509381[\/latex]<\/li>\r\n \t<li>[latex]0.12500938[\/latex]<\/li>\r\n \t<li>[latex]0.11614402[\/latex]<\/li>\r\n \t<li>[latex]0.12406794[\/latex]<\/li>\r\n \t<li>[latex]0.12490631[\/latex]<\/li>\r\n \t<li>[latex]0.12499063[\/latex]<\/li>\r\n<\/ol>\r\n[latex]\\underset{x\\to 2^-}{\\lim}\\frac{1-\\frac{2}{x}}{x^2-4}=0.1250=\\frac{1}{8}[\/latex]<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\u221210.00000[\/latex]<\/li>\r\n \t<li>[latex]\u2212100.00000[\/latex]<\/li>\r\n \t<li>[latex]\u22121000.0000[\/latex]<\/li>\r\n \t<li>[latex]\u221210,000.000;[\/latex]<\/li>\r\n<\/ol>\r\nGuess: [latex]\\underset{\\alpha \\to 0^+}{\\lim}\\frac{1}{\\alpha } \\cos (\\frac{\\pi }{\\alpha })=\\infty[\/latex], Actual: DNE<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202929\/CNX_Calc_Figure_02_02_214.jpg\" alt=\"A graph of the function (1\/alpha) * cos (pi \/ alpha), which oscillates gently until the interval [-.2, .2], where it oscillates rapidly, going to infinity and negative infinity as it approaches the y axis.\" \/><\/li>\r\n \t<li>False; [latex]\\underset{x\\to -2^+}{\\lim}f(x)=+\\infty [\/latex]<\/li>\r\n \t<li>False; [latex]\\underset{x\\to 6}{\\lim}f(x)[\/latex] DNE since [latex]\\underset{x\\to 6^-}{\\lim}f(x)=2[\/latex] and [latex]\\underset{x\\to 6^+}{\\lim}f(x)=5[\/latex].<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]2[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]1[\/latex]<\/li>\r\n \t<li>DNE<\/li>\r\n \t<li>[latex]0[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>DNE<\/li>\r\n \t<li>[latex]2[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]3[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>DNE<\/li>\r\n \t<li><\/li>\r\n \t<li>[latex]0[\/latex]<\/li>\r\n \t<li><\/li>\r\n \t<li>\r\n<p id=\"fs-id1170572435005\">Answers may vary.<\/p>\r\n<span id=\"fs-id1170572435009\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202954\/CNX_Calc_Figure_02_02_209.jpg\" alt=\"A graph of a piecewise function with two segments. The first segment is in quadrant three and asymptotically goes to negative infinity along the y axis and 0 along the x axis. The second segment consists of two curves. The first appears to be the left half of an upward opening parabola with vertex at (0,1). The second appears to be the right half of a downward opening parabola with vertex at (0,1) as well.\" \/><\/span><\/li>\r\n \t<li>\r\n<p id=\"fs-id1170572552619\">Answers may vary.<\/p>\r\n<span id=\"fs-id1170572552623\"><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202957\/CNX_Calc_Figure_02_02_211.jpg\" alt=\"A graph containing two curves. The first goes to 2 asymptotically along y=2 and to negative infinity along x = -2. The second goes to negative infinity along x=-2 and to 2 along y=2.\" \/><\/span><\/li>\r\n<\/ol>","rendered":"<h2 class=\"entry-title\">A Preview of Calculus<\/h2>\n<p id=\"fs-id1170573593926\">For the following exercises (1-3), points [latex]P(1,2)[\/latex] and [latex]Q(x,y)[\/latex] are on the graph of the function [latex]f(x)=x^2+1[\/latex].<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]2.2100000[\/latex]<\/li>\n<li>[latex]2.0201000[\/latex]<\/li>\n<li>[latex]2.0020010[\/latex]<\/li>\n<li>[latex]2.0002000[\/latex]<\/li>\n<li>[latex](1.1000000, 2.2100000)[\/latex]<\/li>\n<li>[latex](1.0100000, 2.0201000)[\/latex]<\/li>\n<li>[latex](1.0010000, 2.0020010)[\/latex]<\/li>\n<li>[latex](1.0001000, 2.0002000)[\/latex]<\/li>\n<li>[latex]2.1000000[\/latex]<\/li>\n<li>[latex]2.0100000[\/latex]<\/li>\n<li>[latex]2.0010000[\/latex]<\/li>\n<li>[latex]2.0001000[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li><\/li>\n<li>[latex]y=2x[\/latex]<\/li>\n<li><\/li>\n<li>[latex]3[\/latex]<\/li>\n<li><\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]2.0248457[\/latex]<\/li>\n<li>[latex]2.0024984[\/latex]<\/li>\n<li>[latex]2.0002500[\/latex]<\/li>\n<li>[latex]2.0000250[\/latex]<\/li>\n<li>[latex](4.1000000,2.0248457)[\/latex]<\/li>\n<li>[latex](4.0100000,2.0024984)[\/latex]<\/li>\n<li>[latex](4.0010000,2.0002500)[\/latex]<\/li>\n<li>[latex](4.00010000,2.0000250)[\/latex]<\/li>\n<li>[latex]0.24845673[\/latex]<\/li>\n<li>[latex]0.24984395[\/latex]<\/li>\n<li>[latex]0.24998438[\/latex]<\/li>\n<li>[latex]0.24999844[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li><\/li>\n<li>[latex]y=\\frac{x}{4}+1[\/latex]<\/li>\n<li><\/li>\n<li>[latex]\\pi[\/latex]<\/li>\n<li><\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\u22120.95238095[\/latex]<\/li>\n<li>[latex]\u22120.99009901[\/latex]<\/li>\n<li>[latex]\u22120.99502488[\/latex]<\/li>\n<li>[latex]\u22120.99900100[\/latex]<\/li>\n<li>[latex](\u22121;.0500000,\u22120;.95238095)[\/latex]<\/li>\n<li>[latex](\u22121;.0100000,\u22120;.9909901)[\/latex]<\/li>\n<li>[latex](\u22121;.0050000,\u22120;.99502488)[\/latex]<\/li>\n<li>[latex](1.0010000,\u22120;.99900100)[\/latex]<\/li>\n<li>[latex]-0.95238095[\/latex]<\/li>\n<li>[latex]\u22120.99009901[\/latex]<\/li>\n<li>[latex]\u22120.99502488[\/latex]<\/li>\n<li>[latex]\u22120.99900100\u00a0[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li><\/li>\n<li>[latex]y=\u2212x-2[\/latex]<\/li>\n<li><\/li>\n<li>[latex]\u221249[\/latex] m\/sec (velocity of the ball is [latex]49[\/latex] m\/sec downward)<\/li>\n<li><\/li>\n<li>[latex]5.2[\/latex] m\/sec<\/li>\n<li><\/li>\n<li>[latex]-9.8[\/latex] m\/sec<\/li>\n<li><\/li>\n<li>[latex]6[\/latex] m\/sec<\/li>\n<li><\/li>\n<li>Under, [latex]1[\/latex] unit<sup>2<\/sup>; over: [latex]4[\/latex] unit<sup>2<\/sup>. The exact area of the two triangles is [latex]\\frac{1}{2}(1)(1)+\\frac{1}{2}(2)(2)=2.5 \\text{ units}^2[\/latex].<\/li>\n<li><\/li>\n<li>Under, [latex]0.96[\/latex] unit<sup>2<\/sup>; over, [latex]1.92[\/latex] unit<sup>2<\/sup>. The exact area of the semicircle with radius [latex]1[\/latex] is [latex]\\frac{\\pi (1)^2}{2}=\\frac{\\pi }{2}[\/latex] unit<sup>2<\/sup>.<\/li>\n<li><\/li>\n<li>Approximately [latex]1.3333333[\/latex] unit<sup>2<\/sup><\/li>\n<\/ol>\n<h2>Introduction to the limit of a function<\/h2>\n<p id=\"fs-id1170572347378\"><strong>In the following exercises (1-3), set up a table of values to find the indicated limit. Round to eight digits.<\/strong><\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\u22120.80000000[\/latex]<\/li>\n<li>[latex]\u22120.98000000[\/latex]<\/li>\n<li>[latex]\u22120.99800000[\/latex]<\/li>\n<li>[latex]\u22120.99980000[\/latex]<\/li>\n<li>[latex]\u22121.2000000[\/latex]<\/li>\n<li>[latex]\u22121.0200000[\/latex]<\/li>\n<li>[latex]\u22121.0020000[\/latex]<\/li>\n<li>[latex]\u22121.0002000;[\/latex]<\/li>\n<\/ol>\n<p>[latex]\\underset{x\\to 1}{\\lim}(1-2x)=-1[\/latex]<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\u221237.931934[\/latex]<\/li>\n<li>[latex]\u22123377.9264[\/latex]<\/li>\n<li>[latex]\u2212333,777.93[\/latex]<\/li>\n<li>[latex]\u221233,337,778[\/latex]<\/li>\n<li>[latex]\u221229.032258[\/latex]<\/li>\n<li>[latex]\u22123289.0365[\/latex]<\/li>\n<li>[latex]\u2212332,889.04[\/latex]<\/li>\n<li>[latex]\u221233,328,889[\/latex]<\/li>\n<\/ol>\n<p>[latex]\\underset{x\\to 0}{\\lim}\\frac{z-1}{z^2(z+3)}=\u2212\\infty[\/latex]<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]0.13495277[\/latex]<\/li>\n<li>[latex]0.12594300[\/latex]<\/li>\n<li>[latex]0.12509381[\/latex]<\/li>\n<li>[latex]0.12500938[\/latex]<\/li>\n<li>[latex]0.11614402[\/latex]<\/li>\n<li>[latex]0.12406794[\/latex]<\/li>\n<li>[latex]0.12490631[\/latex]<\/li>\n<li>[latex]0.12499063[\/latex]<\/li>\n<\/ol>\n<p>[latex]\\underset{x\\to 2^-}{\\lim}\\frac{1-\\frac{2}{x}}{x^2-4}=0.1250=\\frac{1}{8}[\/latex]<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\u221210.00000[\/latex]<\/li>\n<li>[latex]\u2212100.00000[\/latex]<\/li>\n<li>[latex]\u22121000.0000[\/latex]<\/li>\n<li>[latex]\u221210,000.000;[\/latex]<\/li>\n<\/ol>\n<p>Guess: [latex]\\underset{\\alpha \\to 0^+}{\\lim}\\frac{1}{\\alpha } \\cos (\\frac{\\pi }{\\alpha })=\\infty[\/latex], Actual: DNE<img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202929\/CNX_Calc_Figure_02_02_214.jpg\" alt=\"A graph of the function (1\/alpha) * cos (pi \/ alpha), which oscillates gently until the interval [-.2, .2], where it oscillates rapidly, going to infinity and negative infinity as it approaches the y axis.\" \/><\/li>\n<li>False; [latex]\\underset{x\\to -2^+}{\\lim}f(x)=+\\infty[\/latex]<\/li>\n<li>False; [latex]\\underset{x\\to 6}{\\lim}f(x)[\/latex] DNE since [latex]\\underset{x\\to 6^-}{\\lim}f(x)=2[\/latex] and [latex]\\underset{x\\to 6^+}{\\lim}f(x)=5[\/latex].<\/li>\n<li><\/li>\n<li>[latex]2[\/latex]<\/li>\n<li><\/li>\n<li>[latex]1[\/latex]<\/li>\n<li>DNE<\/li>\n<li>[latex]0[\/latex]<\/li>\n<li><\/li>\n<li>DNE<\/li>\n<li>[latex]2[\/latex]<\/li>\n<li><\/li>\n<li>[latex]3[\/latex]<\/li>\n<li><\/li>\n<li>DNE<\/li>\n<li><\/li>\n<li>[latex]0[\/latex]<\/li>\n<li><\/li>\n<li>\n<p id=\"fs-id1170572435005\">Answers may vary.<\/p>\n<p><span id=\"fs-id1170572435009\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202954\/CNX_Calc_Figure_02_02_209.jpg\" alt=\"A graph of a piecewise function with two segments. The first segment is in quadrant three and asymptotically goes to negative infinity along the y axis and 0 along the x axis. The second segment consists of two curves. The first appears to be the left half of an upward opening parabola with vertex at (0,1). The second appears to be the right half of a downward opening parabola with vertex at (0,1) as well.\" \/><\/span><\/li>\n<li>\n<p id=\"fs-id1170572552619\">Answers may vary.<\/p>\n<p><span id=\"fs-id1170572552623\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202957\/CNX_Calc_Figure_02_02_211.jpg\" alt=\"A graph containing two curves. The first goes to 2 asymptotically along y=2 and to negative infinity along x = -2. The second goes to negative infinity along x=-2 and to 2 along y=2.\" \/><\/span><\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":108,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/150"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/150\/revisions"}],"predecessor-version":[{"id":163,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/150\/revisions\/163"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/108"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/150\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=150"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=150"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=150"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}