... functions such as sin, cos and tan; their reciprocals sec, cosec and cot; and exp and log.5.4. Proposition. Let f and g be differentiable at a,andletkbe a constant. Then k.f,f + g and fg are differentiable ... theright hand side converges to23l +23l2, while the left hand side converges to l. But they arethe same sequence, so both limits are the same by Prop 2.6. Thusl =23l +23l2 and so ... sequence convergent?2.3. SUMS, PRODUCTS AND QUOTIENTS 15so this holds eg. for n ≥ N2.NowletN =max(N1,N2), and choose n ≥ N .Thenbothinequalities hold, and |l − m| = |l − an+ an− m|≤|l−an|+|an−m|by...