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The following numeric functions are considered: H (x) = (x ² +2 x) sin (2 / x) g (x) = x / a * [b / x] and f (x) = x ² ([1 / x] + [1 / x ²] ) a, b belong IR * + a: Show that for all x in IR * +:-2x ² + xb: Concluded limit f en0 c: Show that whatever :: x in IR * + -x/ad: Concluded limit g 0 e: Show that for all x in] -1,1 [: | h (x) | ≤ 3 | x | f: Concluded limit h 0
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