MAT137Y1 Midterm: 2003 Test 1 solution

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

Document Summary

Mat 137y, 2003-2004, solutions to test 1: evaluate the following limits. (8%) (i) lim t 1 t3 1 t 1 x2 5 x2 9. Then t3 1 t 1 lim t 1. = lim t 1 (t 1)(t2 + t + 1) t 1. = lim t 1 t2 + t + 1 = 3. 1 + x) x2 5 x2 5 + 1 + x)( (x2 9)( x2 5 + x2 5 1 x x2 5 + (x2 9)( 1 + x) (x + 2)(x 3) (x + 3)(x 3)( x2 5 + Solve the inequality |x 3| + x 9. If x 3, then x 3 + x 9, or x 6. If x < 3, then 3 x + x 9, or 3 9, which is true for all x which satis es the assumption, so x ( . 3. (5%) (a) give the formal e ,d de nition of the statement lim x a.