{"id":250,"date":"2023-10-24T19:41:06","date_gmt":"2023-10-24T23:41:06","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/?post_type=chapter&p=250"},"modified":"2023-10-25T12:27:52","modified_gmt":"2023-10-25T16:27:52","slug":"1171-quiz","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/chapter\/1171-quiz\/","title":{"raw":"1171 Quiz","rendered":"1171 Quiz"},"content":{"raw":"

Math 1171 Quiz<\/span><\/h1>\r\n
    \r\n \t
  1. [10 marks total]<\/strong>\u00a0Use the graph of [latex]\ud835\udc66 = \ud835\udc53 ( \ud835\udc65 )[\/latex] given below to answer all question on this page.<\/li>\r\n<\/ol>\r\n\"\"\"\"<\/span>\r\n<\/colgroup>\r\n\r\n\r\n\r\n
    a)\u00a0[1] <\/strong>[latex]\ud835\udc53 \u2061 ( 3 ) =[\/latex]<\/span><\/td>\r\nb)\u00a0[1]<\/strong> [latex]\\lim _{x \\rightarrow 3} f(x)=[\/latex]<\/span>\r\n\r\n<\/mrow><\/mstyle><\/mstyle>{\"version\":\"1.1\",\"math\":\"\\small \\lim _{x \\rightarrow 3} f(x)=\"}<\/annotation><\/semantics><\/math><\/td>\r\nc)\u00a0[1] <\/strong>[latex]\\lim _{x \\rightarrow-3^{+}} f(x)=[\/latex]<\/span><\/td>\r\n<\/tr>\r\n
    d)\u00a0[1] <\/strong>[latex]\\lim _{x \\rightarrow 0^{+}} f(x)=[\/latex]<\/span>\r\n\r\n<\/mrow><\/mstyle><\/mstyle>{\"version\":\"1.1\",\"math\":\"\\small \\lim _{x \\rightarrow 0^{+}} f(x)=\"}<\/annotation><\/semantics><\/math><\/td>\r\ne)\u00a0[1]<\/strong> [latex]\\lim _{x \\rightarrow 0^{-}} f(x)=[\/latex]<\/span>\r\n\r\n<\/mrow><\/mstyle><\/mstyle>{\"version\":\"1.1\",\"math\":\"\\small \\lim _{x \\rightarrow 0^{-}} f(x)=\"}<\/annotation><\/semantics><\/math><\/td>\r\nf)\u00a0[1] <\/strong>[latex]\\lim _{x \\rightarrow 0} f(x)=[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\ng) [2]<\/strong> Does the limit of\u00a0f\u00a0<\/em>as [latex]\ud835\udc65 \u2192 2[\/latex] exist?\u00a0Support your answer with a statement involving limits.\r\n\r\nh)\u00a0[2]<\/strong> List all\u00a0x-<\/em>values on the interval -4 < x\u00a0<\/em>< 4 where\u00a0f(x)\u00a0<\/em>has a discontinuity and classify each according to its type.<\/span>\r\n\r\n
    \r\n\r\n2.\u00a0[3 marks each; 6 total]<\/strong> Evaluate the following limits, or state that they do not exist.\r\n\r\na) [latex]\\lim _{x \\rightarrow 4} \\frac{x^{2}-6 x+8}{x^{2}+x-20}=[\/latex]\r\n\r\n \r\n\r\nb) [latex]\\lim _{x \\rightarrow 2} \\frac{1-\\frac{1}{x-1}}{x-2}=[\/latex]\r\n\r\n \r\n\r\n \r\n\r\n3.\u00a0[4 marks]<\/strong> Determine the value of the constant\u00a0c<\/em> that will make\u00a0g(x)<\/em> continuous at\u00a0x<\/em> = 3.\r\n\r\n[latex]g(x)=\\left\\{\\begin{array}{ll}\r\n\\frac{\\sqrt{x+1}-2}{x-3} & \\text { if } x \\neq 3 \\\\\r\n2 c+1 & \\text { if } x=3\r\n\\end{array}\\right.[\/latex]","rendered":"

    Math 1171 Quiz<\/span><\/h1>\n
      \n
    1. [10 marks total]<\/strong>\u00a0Use the graph of [latex]\ud835\udc66 = \ud835\udc53 ( \ud835\udc65 )[\/latex] given below to answer all question on this page.<\/li>\n<\/ol>\n

      \"\"\"\"<\/span><\/p>\n\n\n\n\n<\/colgroup>\n\n\n\n
      a)\u00a0[1] <\/strong>[latex]\ud835\udc53 \u2061 ( 3 ) =[\/latex]<\/span><\/td>\nb)\u00a0[1]<\/strong> [latex]\\lim _{x \\rightarrow 3} f(x)=[\/latex]<\/span><\/p>\n

      <\/mrow><\/mstyle><\/mstyle>{“version”:”1.1″,”math”:”\\small \\lim _{x \\rightarrow 3} f(x)=”}<\/annotation><\/semantics><\/math><\/td>\nc)\u00a0[1] <\/strong>[latex]\\lim _{x \\rightarrow-3^{+}} f(x)=[\/latex]<\/span><\/td>\n<\/tr>\n

      d)\u00a0[1] <\/strong>[latex]\\lim _{x \\rightarrow 0^{+}} f(x)=[\/latex]<\/span><\/p>\n

      <\/mrow><\/mstyle><\/mstyle>{“version”:”1.1″,”math”:”\\small \\lim _{x \\rightarrow 0^{+}} f(x)=”}<\/annotation><\/semantics><\/math><\/td>\ne)\u00a0[1]<\/strong> [latex]\\lim _{x \\rightarrow 0^{-}} f(x)=[\/latex]<\/span><\/p>\n

      <\/mrow><\/mstyle><\/mstyle>{“version”:”1.1″,”math”:”\\small \\lim _{x \\rightarrow 0^{-}} f(x)=”}<\/annotation><\/semantics><\/math><\/td>\nf)\u00a0[1] <\/strong>[latex]\\lim _{x \\rightarrow 0} f(x)=[\/latex]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      g) [2]<\/strong> Does the limit of\u00a0f\u00a0<\/em>as [latex]\ud835\udc65 \u2192 2[\/latex] exist?\u00a0Support your answer with a statement involving limits.<\/p>\n

      h)\u00a0[2]<\/strong> List all\u00a0x-<\/em>values on the interval -4 < x\u00a0<\/em>< 4 where\u00a0f(x)\u00a0<\/em>has a discontinuity and classify each according to its type.<\/span><\/p>\n

      \n

      2.\u00a0[3 marks each; 6 total]<\/strong> Evaluate the following limits, or state that they do not exist.<\/p>\n

      a) [latex]\\lim _{x \\rightarrow 4} \\frac{x^{2}-6 x+8}{x^{2}+x-20}=[\/latex]<\/p>\n

       <\/p>\n

      b) [latex]\\lim _{x \\rightarrow 2} \\frac{1-\\frac{1}{x-1}}{x-2}=[\/latex]<\/p>\n

       <\/p>\n

       <\/p>\n

      3.\u00a0[4 marks]<\/strong> Determine the value of the constant\u00a0c<\/em> that will make\u00a0g(x)<\/em> continuous at\u00a0x<\/em> = 3.<\/p>\n

      [latex]g(x)=\\left\\{\\begin{array}{ll} \\frac{\\sqrt{x+1}-2}{x-3} & \\text { if } x \\neq 3 \\\\ 2 c+1 & \\text { if } x=3 \\end{array}\\right.[\/latex]<\/p>\n","protected":false},"author":1655,"menu_order":8,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-250","chapter","type-chapter","status-publish","hentry"],"part":73,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/chapters\/250","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/wp\/v2\/users\/1655"}],"version-history":[{"count":14,"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/chapters\/250\/revisions"}],"predecessor-version":[{"id":254,"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/chapters\/250\/revisions\/254"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/parts\/73"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/chapters\/250\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/wp\/v2\/media?parent=250"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=250"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/wp\/v2\/contributor?post=250"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/wp-json\/wp\/v2\/license?post=250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}