The Calculus with Analytic Geometry, Volume 1Harper & Row, 1981 - Calculus |
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Page 529
... HYPERBOLIC FUNCTIONS 9.7.1 Definition Certain combinations of e * and e- * appear so frequently in applications of mathematics that they are given special names . Two of these functions are the hyperbolic sine function and the hyperbolic ...
... HYPERBOLIC FUNCTIONS 9.7.1 Definition Certain combinations of e * and e- * appear so frequently in applications of mathematics that they are given special names . Two of these functions are the hyperbolic sine function and the hyperbolic ...
Page 537
Louis Leithold. 54. Prove that the hyperbolic sine function is continuous and ... cosine function is continuous on its entire domain but is not monotonic on its entire domain . Find the intervals on which the ... HYPERBOLIC FUNCTIONS 537.
Louis Leithold. 54. Prove that the hyperbolic sine function is continuous and ... cosine function is continuous on its entire domain but is not monotonic on its entire domain . Find the intervals on which the ... HYPERBOLIC FUNCTIONS 537.
Page 538
... functions were defined in terms of the exponential function , and the natural logarithmic function is the inverse of the exponential function . Following are these expressions for sinh - 1 , cosh 538 9 TRIGONOMETRIC AND HYPERBOLIC ...
... functions were defined in terms of the exponential function , and the natural logarithmic function is the inverse of the exponential function . Following are these expressions for sinh - 1 , cosh 538 9 TRIGONOMETRIC AND HYPERBOLIC ...
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absolute maximum value absolute minimum absolutely convergent antiderivative chain rule closed interval convergent coordinates cos² cosh cost function curve defined by f(x definite integral derivative differentiable directrix distance Draw a sketch elements of area ellipse evaluate Example exists f is continuous FIGURE Find an equation Find the area Find the volume focus following theorem formula function defined function f Given f(x graph of ƒ Hence hyperbola ILLUSTRATION intersection inverse L'Hôpital's rule lim f(x Limit Theorem measure natural logarithmic obtain open interval parabola particle perpendicular polar positive number power series Proof Prove radius real numbers rectangle rectangular elements region bounded relative maximum value revolving Riemann sum sec² sequence shown in Fig Simpson's rule sin² sinh slope solid of revolution Solution square units tangent line tank velocity vertex vertices x₁ y₁