MAT102H5 Chapter Notes -Jyj, Bounded Function
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MAT102H5 Full Course Notes
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Mat102s - introduction to mathematical proofs - utm - spring 2011. Solutions to selected problems from problem set c: 1. 17. The domain of y = |x| is r (every number has an absolute value). The image is [0, ) since every y 0 is the absolute value of itself: y = |y| . 1. 35. x/y + y/x 2 if and only if x and y have the same sign: if x or y is 0, then the expression is unde ned. If they have opposite signs, then the left side is negative. If they have the same sign, then multiplying by xy yields x2 + y2 2xy, equivalent to x2 2xy + y2 0, equivalent to (x y)2 0. The last inequality holds whenever x and y have the same sign, so this necessary condition is also su cient. If f and g are bounded, then there exist m1 and m2, such that |f (x)| m1 and.
