cos(x) = 1 - x^{2}/2! + x^{4}/4! - x^{6}/6! + ... sin(x) = x/1! - x^{3}/3! + x^{5}/5! - x^{7}/7! + ... cosh(x) = 1 + x^{2}/2! + x^{4}/4! + x^{6}/6! + ... sinh(x) = x/1! + x^{3}/3! + x^{5}/5! + x^{7}/7! + ... sinh(x)-sin(x)=2x^{3}/3!+...... cosh(x)-cos(x)=2x^{2}/2! +..... lim_{x->0} ( sinh(x)-sin(x) /x(cosh(x)-cos(x)) lim_{x}->0 (2x^{3}/3!)/x*(2*x^{2}/2! )=2/3!= 1/3
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