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7Product rule Dt[f[x]g[x],x]== Limit[(f[x+t]g[x+t]-f[x]g[x])/t,t->0]== Limit[(f[x+t]g[x+t]-f[x+t]g[x]+f[x+t]g[x]-f[x]g[x])/t,t->0]== Li
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1Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesim
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00 < x < Pi/2 Sin[x] < x < Tan[x] Csc[x] > 1/x > Cot[x] 1 > Sin[x]/x > Cos[x] Limit[Cos[x], x -> 0 ] == 1 Limit[Si
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0k==Limit[f[x]/g[x],x->c] 0==Limit[f[x],x->c]-k Limit[g[x],x->c]==Limit[f[x]-k g[x],x->c] 0==Limit[f'[x]-k g'[x],x->c] Limit[f
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1F[1]==F[2]==1 F[n+2]==F[n+1]+F[n] F[n]==((1+Sqrt[5])^n-(1-Sqrt[5])^n)/(2^n Sqrt[5])
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1E == Limit[(1/n + 1)^n, n -> Infinity] == Limit[Sum[(1/n)^i*Binomial[n, i], {i, 0, n}], n -> Infinity] == Limit[Sum[(n!*(1/n)^i)/(i!*(
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0a != 1 Sum[i*a^i, {i, 1, n}] == ((a - 1)*Sum[i*a^i, {i, 1, n}])/(a - 1) == (Sum[i*a^(i + 1), {i, 1, n}] - Sum[i*a^i, {i, 1, n}])/(a - 1) ==
