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+ /><line y2="381.4" style="fill:none;" x1="91" x2="96.43" y1="381.4"
+ /><line y2="338.6" style="fill:none;" x1="91" x2="96.43" y1="338.6"
+ /><line y2="295.8" style="fill:none;" x1="91" x2="96.43" y1="295.8"
+ /><line y2="253" style="fill:none;" x1="91" x2="96.43" y1="253"
+ /><line y2="210.2" style="fill:none;" x1="91" x2="96.43" y1="210.2"
+ /><line y2="167.4" style="fill:none;" x1="91" x2="96.43" y1="167.4"
+ /><line y2="124.5999" style="fill:none;" x1="91" x2="96.43" y1="124.5999"
+ /><line y2="81.8" style="fill:none;" x1="91" x2="96.43" y1="81.8"
+ /><line y2="39" style="fill:none;" x1="91" x2="96.43" y1="39"
+ /><line y2="467" style="fill:none;" x1="634" x2="628.57" y1="467"
+ /><line y2="424.2" style="fill:none;" x1="634" x2="628.57" y1="424.2"
+ /><line y2="381.4" style="fill:none;" x1="634" x2="628.57" y1="381.4"
+ /><line y2="338.6" style="fill:none;" x1="634" x2="628.57" y1="338.6"
+ /><line y2="295.8" style="fill:none;" x1="634" x2="628.57" y1="295.8"
+ /><line y2="253" style="fill:none;" x1="634" x2="628.57" y1="253"
+ /><line y2="210.2" style="fill:none;" x1="634" x2="628.57" y1="210.2"
+ /><line y2="167.4" style="fill:none;" x1="634" x2="628.57" y1="167.4"
+ /><line y2="124.5999" style="fill:none;" x1="634" x2="628.57" y1="124.5999"
+ /><line y2="81.8" style="fill:none;" x1="634" x2="628.57" y1="81.8"
+ /><line y2="39" style="fill:none;" x1="634" x2="628.57" y1="39"
+ /></g
+ ><g transform="translate(84.3333,467)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-24" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.5</text
+ ></g
+ ><g transform="translate(84.3333,424.2)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.52</text
+ ></g
+ ><g transform="translate(84.3333,381.4)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.54</text
+ ></g
+ ><g transform="translate(84.3333,338.6)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.56</text
+ ></g
+ ><g transform="translate(84.3333,295.8)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.58</text
+ ></g
+ ><g transform="translate(84.3333,253)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-24" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.6</text
+ ></g
+ ><g transform="translate(84.3333,210.2)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.62</text
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+ ><g transform="translate(84.3333,167.4)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.64</text
+ ></g
+ ><g transform="translate(84.3333,124.5999)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.66</text
+ ></g
+ ><g transform="translate(84.3333,81.8)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-33" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.68</text
+ ></g
+ ><g transform="translate(84.3333,39)" style="font-size:16.6667px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-24" xml:space="preserve" y="6.5" style="stroke:none;"
+ >0.7</text
+ ></g
+ ><g transform="translate(46.3333,252.9998) rotate(-90)" style="font-size:18.3333px; fill:rgb(38,38,38); text-rendering:geometricPrecision; color-rendering:optimizeQuality; image-rendering:optimizeQuality; stroke:rgb(38,38,38); color-interpolation:linearRGB;"
+ ><text x="-13.5" xml:space="preserve" y="-5" style="stroke:none;"
+ >f(x)</text
+ ></g
+ ><g style="stroke-linecap:butt; fill:rgb(0,114,189); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(0,114,189); color-interpolation:linearRGB; stroke-width:0.8333;"
+ ><path d="M91 467 L119.579 373.4814 L148.1579 296.6363 L176.7368 237.4048 L205.3158 191.7797 L233.8947 156.7113 L262.4737 129.8598 L291.0526 109.4154 L319.6316 93.9697 L348.2105 82.4194 L376.7895 73.8966 L405.3684 67.7155 L433.9474 63.3316 L462.5263 60.312 L491.1053 58.3114 L519.6842 57.0543 L548.2632 56.3201 L576.8421 55.9331 L605.421 55.7526 L634 53.665" style="fill:none; fill-rule:evenodd;"
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+ /></g
+ ><g style="fill:white; text-rendering:optimizeSpeed; color-rendering:optimizeSpeed; image-rendering:optimizeSpeed; shape-rendering:crispEdges; stroke:white; color-interpolation:sRGB;"
+ ><path style="stroke:none;" d="M621 98 L621 52 L509 52 L509 98 Z"
+ /></g
+ ><g transform="translate(567.8814,64.6027)" style="text-rendering:geometricPrecision; font-size:15px; color-interpolation:linearRGB; color-rendering:optimizeQuality; image-rendering:optimizeQuality;"
+ ><text x="0" xml:space="preserve" y="6" style="stroke:none;"
+ >Approx</text
+ ></g
+ ><g style="stroke-linecap:butt; fill:rgb(0,114,189); text-rendering:geometricPrecision; image-rendering:optimizeQuality; color-rendering:optimizeQuality; stroke-linejoin:round; stroke:rgb(0,114,189); color-interpolation:linearRGB; stroke-width:0.8333;"
+ ><line y2="64.6027" style="fill:none;" x1="514.0112" x2="564.123" y1="64.6027"
+ /></g
+ ><g transform="translate(567.8814,85.3973)" style="text-rendering:geometricPrecision; font-size:15px; color-interpolation:linearRGB; color-rendering:optimizeQuality; image-rendering:optimizeQuality;"
+ ><text x="0" xml:space="preserve" y="6" style="stroke:none;"
+ >Exact</text
+ ></g
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+ /><path d="M509 98 L509 52 L621 52 L621 98 Z" style="fill:none; fill-rule:evenodd; stroke:rgb(38,38,38); stroke-linejoin:miter;"
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+ ></g
+></svg
+>
%% Section 2
-N = 5;
+N = 20;
x = linspace(1,2, N);
h = x(2) - x(1);
answer = [0.5;answer;log(2)];
plot(x, answer);
+
+
hold on;
real_values = zeros(N, 1);
for i=1:N
real_values(i) = (4/x(i)) - (2/(x(i)^2)) + log(x(i)) - (3/2);
end
plot(x, real_values);
-
-
+xlabel("x");
+ylabel("f(x)");
+legend(["Approx"; "Exact"]);
norm(answer - real_values, inf)
\ No newline at end of file