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7.6 The Hyperbolic Functions Return To Contents Go To Problems & Solutions The hyperbolic functions are defined in terms of the natural exponential function ex. For example, the hyperbolic sine function is defined as (ex – e–x)/2 and denoted sinh, pronounced “ shin ”, so that sinh x = (ex – e–x)/2. Definition 1.1 We’ll […]
12.7 Areas Of Surfaces Of Revolution Return To Contents Go To Problems & Solutions 1. Surfaces Of Revolution Consider a sphere of radius r. See Fig. 1.1. We wish to find the surface area of this sphere. For this purpose we set up an xy-coordinate system in such a way that its origin is at […]
16.2.2 Equations With Variable Coefficients – Reduction Of Order Return To Contents Go To Problems & Solutions 1. Second-Order Linear Homogeneous Differential Equations With Variable Coefficients In this section, we’ll use the abbreviations: “DE” for “differential equation”, “GS” for “general solution”, “HDE” for “homogeneous differential equation”, and “HE” for “homogeneous equation”. Recall that a second-order […]
