Hi Dennis,
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 =
9.99910000620829e06 and g = 1.00001999980837e05 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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