### Introduction

CE5

The derivative f″(x) of the function f(x) at the point P represents the slope of the tangent line at that point.

CE5The area under the curve y=f(x) may be found by calculating the sum of the elements of area ΔA, whose width is ΔX and whose height is f(x).

calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. The English physicist Isaac Newton and the German mathematician G. W. Leibniz, working independently, developed the calculus during the 17th cent. The calculus and its basic tools of differentiation and integration serve as the foundation for the larger branch of mathematics known as analysis. The methods of calculus are essential to modern physics and to most other branches of modern science and engineering.

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