MAT137Y1 Midterm: 2009 Test 1 solution

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

Document Summary

Mat137y, 2009 2010 winter session, solutions to term test 1: evaluate the following limits. (do not prove them using the formal de nition of limit. ) Obtaining a common denominator and factoring the denominator, we get x2 x 12. = lim x 4 lim x 4 x x2 5x + 5 x 1 (10%) (ii) lim x 1. We multiply top and bottom by both conjugates, giving us x x2 5x + 5 x 1 x2 5x + 5 x2 5x + 5 x + 1 x + 1. [x2 (x2 5x + 5)]( x + 1) x2 5x + 5) (x 1)(x + 5( x + 1) x2 5x + 5. = lim x 1 (10%) (i) suppose is in the rst quadrant, and cos = 1: find the exact value of sin2 . We can do this by drawing a triangle. Alternatively, since sin2 + cos2 = 1, we have sin2 = 1 cos2 = 1 1.