MAT137Y1 Midterm: 2009 Test 2 solution

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: N/ A

Document Summary

Mat 137y, 2008-2009 winter session, term test 2 solutions: evaluate the following limits, or show the limit does not exist. (cid:19) (cid:18) cotx 1 x (8%) (i) lim x 0. Sinx xcosx xsinx cosx + cosx xsinx sinx + xcosx sinx + xcosx. 2 cosx xsinx cosx x2 + cosx x2 + 2009 (8%) (ii) lim x . Since 1 cosx 1, we have so by the squeeze theorem, lim x x2 1 x2 + 2009 x2 + cosx x2 + 2009. = 1. (note, applying l"h opital"s rule twice yields lim x . L"h opital"s rule does not apply in this situation. ) , which does not exist, but (15%) 2. Recall that the volume of a right circular cone is v = 1. 3 r2h, where r is the radius of the (circular) base, and h is the height of the cone.