9687 /www/nrich/html/content/id/9687/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image src="icon.png"></mdo:image> <div ng-app="app" ng-controller="Ctrl"> <p>Here, to 3 significant figures, are 2 functions of</p> <p class="display">$x = $ <input class="xinput" max="10" min="-10" ng-model="x" type="number"></input></p> <p class="display">$f(x) = $ <span class="mgc-eval" f="x-&gt;3*sin(x)+2" sigfigs="3"> </span>,</p> <p class="display">$g(x) = $ <span class="mgc-eval" f="x-&gt;2*x-2" sigfigs="3"> </span></p> <p><i>Before continuing, see if you can get to know these functions better. Use scrolling controls on the x input box to give you access to lots of values quickly. You can type in decimal values.</i></p> <ol> <li> <p>Experiment until you find a value of $x$ where $f(x)$ appears to be the same as $g(x)$.</p> <p>How did you narrow the possibilities down to this value of $x$? Is there a general method?</p> <p>How close do you think $f(x)$ and $g(x)$ really are at this value? Can you find a value of $x$ where $f(x)$ should be even closer to $g(x)$?</p> </li> <li> <p>Here, again to 3 significant figures, are two more functions of</p> <p class="display">$x = $ <input class="xinput" max="10" min="-10" ng-model="x" type="number"></input>.</p> <p class="display">$f(x) = $ <span class="mgc-eval" f="x-&gt;3*sin(x)+2" sigfigs="3"> </span> as before, but also:</p> <p class="display">$h(x) = $ <span class="mgc-eval" f="x-&gt;x/4-0.2" sigfigs="3"> </span></p> <p class="display">$j(x) = $ <span class="mgc-eval" f="x-&gt;x*x-25" sigfigs="3"> </span></p> <p>Experimentally, find values of $x$ and $y$ so that $f(x) = h(x)$ and $f(y) = j(y)$. Compare your findings with others and discuss.</p> </li> <li> <p>What sorts of function are $f, g, h,$ and $j$? Can you find write down expressions for $f, g, h$ and $j$?</p> </li> </ol> </div></mdoxml> 2 3 0 0 0 1 0 Can you solve these simultaneous equations without knowing what the equations are?