MATH 151 Midterm: MATH 151 TAMU Y2015 2015a X1A Solutions
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3 c(cid:13)2015 art belmonte: (a) the average rate of change of f (x) = sin2 x over. 3 : (d) we have = bac = cos 1 ab ac. = cos 1(cid:16) [2, 1] [3, 5: (b) the tangent line to f (x) at x = 5 is y = 7 is m = 7. =(cid:12)(cid:12)(cid:12: (d) the line y = 3x 4 contains point b (2, 2) and has direction vector v = [1, 3], the orthogonal complement of which is v = [ 3, 1]. B is w = b a = [1, 0]. The distance from the point a to the line is |compv w| =(cid:12)(cid:12)(cid:12)(cid:12) kv k(cid:12)(cid:12)(cid:12)(cid:12) 5 and thus t = 8 2(cid:0) 1: (a) now c = sa + tb yields the vector equation. [8, 7] = s [2, 3] + t [1, 1] or scalar equations. 2s + t = 8 and 3s t = 7.
