Main Content

Homework and Webwork Hints & Help

This is a collection of frequently & infrequently asked questions, and their answers.

• Please update (add) your email address on the webwork server, so that when you send me a question I can send the reply straight to your email instead of via the webwork server (which occasionally has "issues" delivering messages.)
• If "0.123" is the correct answer, webwork will mark ".123" as incorrect.
• If "1E-14" is the correct answer, webwork will mark "1e-14" as incorrect (it evaluates to 1*e - 14 = -11.281...)
• Webwork (usually) expects 4-5 digits in the anwers, so "0.0012" may be marked wrong if webwork expects "0.0012345." To show more digits in matlab issue the command format long before you start computing.

• Leading zeros are not "digits," so "0.123" specifies 3 digits.
• We have to round in each step since you can never keep more than the specified number of digits, so
  • a * ( b + c ) = round( round(a) * round( round(b) + round(c) ))
• Ponder (in 4-digit rounding)
  • (1.000 + 0.0004000) + 0.0001000 = 1.000 + 0.0001000 = 1.000
  • (0.0001000 + 0.0004000 + 1.000) = 0.0005000 + 1.000 = 1.001
  so, what is the SAME in exact arithmetic is not necessarily the same in floating point arithmetic.
• Webwork does (should) recognize multiple forms of your solutions, but nothing is perfect - so if you are convinced you have the right answer and is denied by webwork, let me know.

• For bisection
  • m_k = ( a_k + b_k ) / 2
  i.e. the indices have to match.
• The root is the "solution" so unless we have moved the update of the approximation of the root |x_k-x_k-1| < tol, we should not stop, even though we may have |f(x_k)| < tol.

• It appears that machine-epsilon in webwork and matlab are different (unverified); this, or something else, is causing correct small values (of size 1E-14 and smaller) from matlab to be marked as incorrect (*:rolleyes:*). If you have the correct final x_n, but an "incorrect" value for f(x_n), send me an email (and I'll repsond with the value that webwork expects).

• A few students have found that they got "correct" values for f[x₀,x₁], f[x₁,x₂], f[x₁,x₂], f[x₀,x₁,x₂], f[x₁,x₂,x₃], and in some cases also for P3(x) but an "incorrect" value for f[x₀,x₁,x₂,x₃]. So far it has been exclusively due to typos in the digits (and in one case a print-out had truncated digits) for the data points. This turned into a good illustration of how higher derivatites are sensitive to roundoff (or typo) "noise;" here the 1^st, and 2^nd divided differences fall within webwork's tolerance for answer checking, and the 3^rd outside.

• If you have everything right, except maybe one or two coefficients; do format long, and re-run to see more digits...

• Version 1 had too many bugs... Fear not, HW #8 will return to wEbWoRk...