MAT137Y1 Midterm: 2009 Summer Test 2 solution

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

Document Summary

Mat137: term test 2 answers: (a) function f(x) is di erentiable at c if limh 0 f (c+h) f (c) h exists. (b) use your de nition from part (a) to prove f(x) = sin(x) is di erentiable at c. See the textbook, page 142: (a) find the equation of the line tangent to the curve 2x3 + 2y3 = 9xy at the point (1, 2). The answer is y = 4 (b) let function g( ) = |1 tan( )| have domain (cid:8)0, . 2 and domain of derivative dg d . = d|u| dg d du d du where u = 1 tan( ) (cid:17) (cid:17) Since du d = sec2( ), this proves, The derivative of |u| is 1 and de ned whenever u (cid:54)= 0. 1 tan( ) > 0 tan( ) < 1 (cid:110) 1 tan( ) < 0 tan( ) > 1 (cid:16) x = 3x(cid:0) 2x 1 for (cid:110) for (cid:16) .