MAT137Y1 Midterm: 2006 Test 2 solution

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

Document Summary

Mat 137y, 2006 2007 winter session, solutions to term test 2. 1. (9%) (i) find the equation of the tangent line to the graph of y = secx 2cosx at the point ( . 3 = 2 (9%) (ii) for the equation x2 + 4xy + y3 + 5 = 0, nd. Differentiating implicitly, we have 2x + 4x dy us y0 = secxtanx + 2sinx, so the slope of the tangent line is y0( . Thus the equation of the tangent line is y 1 = 3. 3 ) or y = 3 d2y dx2 at the point (2, 1). (cid:12)(cid:12)(cid:12)(cid:12)(2, 1) dx + 4y + 3y2 dy. = 0 = dy dy dx dx (cid:19)2. 2 + 4x d2y dx2 + 4 dy dx. + 3y2 d2y dx2 = 0. (cid:18)dy dx dx = 0. Plugging in x = 2, y = 1 gives.