MAT137Y1 Midterm: 2009 S Test1 solution

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

Document Summary

Mat137: term test 1 answers: calculate tan(cid:0) . 1: let f(x) = x2 + 5 with domain(f) = ( , + ), g(x) = 1 x with domain(g) = ( , 1] and h(x) = 2 cos(x) with domain(h) = [0, 2 ]. Give the formula and domain of f g h(x). For h(x) to be in domain(g), need 2 cos(x) 1 cos(x) 1: by inspection of the unit circle, cos(x) 1, note cos(cid:0) (cid:1) = 1. For g(x) to be in domain(f), do not need any further restriction. f g h(x) = f(cid:0) x h . 1 h(cid:1) (x) = (1 h(x)) + 5, so we have, f g h(x) = 6 2 cos(x) with domain x h i. 3: prove that for all n 1, Hypo let statement s(n) be true for some n 1. 1 (n + 1)((n + 1) + 1) (n + 1) (n + 1) + 1 , which is statement s(n+1).