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Editing Comments

9B Sample 1: 3.a) Step 2, should say 2 - cos(x), not 1 - cos(x) 4. Foundation, would be better to write it as sin^2(x) + cos^2(x) = 1 since you remind them of this in each example before using it anyways 4.b) I think it would look better if you wrote \int 1 dx instead of just \int dx in steps 1 and 3 4.b) Make the size of the final integral in step 4 larger 6.b) Should be limit as a approaches 4 from the left only 7. Foundation, should have a dx at the end of the equation for ds 7.b) Why not solve it using u-sub directly instead of trig sub to start?

9B Sample 2: 4. This is completely blank. 5.b) Just compute 27^2/2^2 = 729/4, would look better I think 7.a) and b) Why convert the limit from a to x, since a ranges over real numbers also so l'Hopital's rule holds. 7.b) Should be limit as a approaches 0 from the right only

9A Sample 1: 1. Foundation, limit as x approaches any value a, not just infinity. And I don't think we need the comment that lim f'(x)/g'(x) is finite or +-infinity.

9A Sample 2: 1. Foundation, limit as x approaches any value a, not just infinity. And I don't think we need the comment that lim f'(x)/g'(x) is finite or +-infinity. 1.a) %if% we plug in x=4... 3.c) Why not just use implicit differentiation to explain how to do the derivative? 5. This is completely blank. 8. Foundation, limit as x approaches any value a, not just infinity. And I don't think we need the comment that lim f'(x)/g'(x) is finite or +-infinity. 10.c) Better to take the limit as x approaches infinity and negative infinity to show the HA is y=0.