** Using WeBWorK **

First, Library/maCalcDB/setLimitsRates2Limits/ur_lr_2_10.pg with seed 3524 gives a 3rd question where one is finding $lim_{x to 2^-} f(x)/g(x)$ where $f,g$ are defined by graphs. The limit of both functions is 0 and $f(x) geq 0$ and $g(x) > 0$ to the left of 2. So it looks like the answer should be 0, or maybe DNE, or maybe something positive. But instead the computer thinks the correct answer is -1.

Second, ibrary/maCalcDB/setDerivatives1_5Tangents/ur_dr_1_5_10.pg just doesn't correctly display the last line as LaTeX math.

Thanks for the great software. -Dennis

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Thanks for the bug report. There certainly appears to be a bug in setLimitsRates2Limits/ur_lr_2_10.pg but looking closer at the code of the problem, the situation really is that the graphs are not displayed with sufficient resolution to see what is going on. The graphs are actually spline curves and I'm pretty sure that the left hand derivative of f at 2 is 1 so that f is negative just to the left of 2. I have checked (since it's easy) that at x = 1.99999, f = -9.99910000620829e-06 and g = 1.00001999980837e-05 and using this WeBWorK guesses that the limit is -1. This is a complicated problem and it is difficult for the author visualize all the possibilities. Changing the resolution of the displayed graphs by adding the option size =>[500,500], i.e.

$graphf = init_graph(-2,-2,5,5,grid =>[7,7], axes => [0,0], size =>[500,500]);
$graphg = init_graph(-2,-2,5,5,,grid =>[7,7], axes => [0,0], size =>[500,500]);

shows, at least in your case, that the answer appears to be -1. Hopefully this resolution will be sufficient for all cases.

For your second bug, you must be using WeBWorK 2 with an old version of setDerivatives1_5Tangents/ur_dr_1_5_10.pg. You can grab a new version of the problem from the CVS (better yet update your whole problem library) or edit the problem replacing the deprecated ${BM} and ${EM} with \( and \) respectively.

Arnie

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