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Some Historical Notes
Elementary Investigation of Functions
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abscissa absolute value absolutely convergent algebraic analytic arctan argument asymptote called circle co-ordinate coefficients constant continuous function convergent convergent series convex corresponding curvature curve curvilinear trapezoid decreasing defined definite integral derivative differential discontinuity divergent domain of definition elementary functions equal equation example exists exponential function expression fact ff(x)dx finite number fraction function f(x geometrical given graph Hence improper integral increasing increment indefinitely independent variable inequality infinitely large magnitude infinitesimal infinity instance integrand inverse length Let us find limit logarithmic mathematical analysis maximum error method negative neighbourhood Newton-Leibniz formula obtained ordinate parabola point x0 polynomial positive number power series problem Proof radius rate of change rational function right-hand side segment straight line sub-interval tangent Taylor series Taylor's formula tends to zero theorem trigonometric functions uniformly convergent vanishes velocity whilst