MATH 171 Final: Math 171 TAMU Spring 15 FinalExamM171SolutionsSpring 15
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26 (d) we can express ~x as a sum of two vectors ~u and ~v, where ~u is parallel to ~y and ~v is perpendicular to ~y. ~v = ~x proj~y~x = h2, 3i . 2 h1, 1i: (30) compute the following limits: (a) lim x 0 sin 2x x (b) lim x 0. 1 x (c) lim x x2ex lim x lim x 0 sin 2x x. 1 x = 1 lim x 0 x2ex = lim x (cid:18) x2 e x(cid:19) = lim x (cid:18) 2x. E x(cid:19) = lim x (cid:18) 2 e x(cid:19) = 0 (d) lim n n(n + 1)(3n + 1) n3 lim n n(n + 1)(3n + 1) n3. 1 n2(cid:19) = 3 (e) lim x 0+ x ln x lim x 0+ x ln x = lim x 0+ ln x. = lim x 0+ ( x) = 0 (f) lim. 2 x(cid:19)x x (cid:18)1 + x (cid:18)x ln(cid:18)1 + lim.
