1. Mathematical Tables1916 - Engineering - 186 pages |
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Page 87
... Derivatives and Differentials .. 157 Lengths and Areas of Plane Figures . 105 Maxima and Minima .. 159 Surfaces and Volumes of Solids ..... 107 Expansion in Series .. 160 Indeterminate Forms .. 163 ALGEBRA Curvature .. 163 Formal ...
... Derivatives and Differentials .. 157 Lengths and Areas of Plane Figures . 105 Maxima and Minima .. 159 Surfaces and Volumes of Solids ..... 107 Expansion in Series .. 160 Indeterminate Forms .. 163 ALGEBRA Curvature .. 163 Formal ...
Page 127
... derivative of w with respect to z is defined as dw / dz = - = lim { [ f ( z + Az ) − f ( z ) ] / Az } when Az approaches 0 . It can be shown that lim { [ exp Az 1 ] / Az } = 1 ; hence d ( e2 ) e2dz , d ( sin z ) = cos z dz , etc. , so ...
... derivative of w with respect to z is defined as dw / dz = - = lim { [ f ( z + Az ) − f ( z ) ] / Az } when Az approaches 0 . It can be shown that lim { [ exp Az 1 ] / Az } = 1 ; hence d ( e2 ) e2dz , d ( sin z ) = cos z dz , etc. , so ...
Page 156
... plane , the development of the helix will be a straight line , with slope equal to tan v . 6 ' 2 ' Helix . FIG . 80 . DIFFERENTIAL AND INTEGRAL CALCULUS DERIVATIVES AND DIFFERENTIALS Derivatives and Differentials 156 ANALYTICAL GEOMETRY.
... plane , the development of the helix will be a straight line , with slope equal to tan v . 6 ' 2 ' Helix . FIG . 80 . DIFFERENTIAL AND INTEGRAL CALCULUS DERIVATIVES AND DIFFERENTIALS Derivatives and Differentials 156 ANALYTICAL GEOMETRY.
Page 157
Edward Vermilye Huntington, Louis Albert Fischer. DIFFERENTIAL AND INTEGRAL CALCULUS DERIVATIVES AND DIFFERENTIALS Derivatives ... derivative of a function y = f ( x ) may be denoted by f ' ( x ) , or by dy / dx . The value of the derivative ...
Edward Vermilye Huntington, Louis Albert Fischer. DIFFERENTIAL AND INTEGRAL CALCULUS DERIVATIVES AND DIFFERENTIALS Derivatives ... derivative of a function y = f ( x ) may be denoted by f ' ( x ) , or by dy / dx . The value of the derivative ...
Page 158
... Derivatives of Higher Orders . The derivative of the derivative is called the second derivative ; the derivative of this , the third derivative ; and . on . Notation : if y = · f ( x ) , SO f ' ( x ) = Day = dy dx ' f ' ( x ) = Dxy ...
... Derivatives of Higher Orders . The derivative of the derivative is called the second derivative ; the derivative of this , the third derivative ; and . on . Notation : if y = · f ( x ) , SO f ' ( x ) = Day = dy dx ' f ' ( x ) = Dxy ...
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Common terms and phrases
9 Avg angle asymptotes axes axis binomial coefficients bisects body of table chord coefficients COMMON LOGARITHMS computation correct to four corresponding cosh Cosines Cotangents CUBE ROOTS CUBE ROOTS continued curvature curve cx² decimal point denoted diam diameter diff differential distance divide draw ellipse equal equivalent to moving Explanation of Table formula four figures fraction gram hyperbolic kilogram length logarithms loge machine meters Method moving it THREE Moving the decimal multiplication nth root parabola parallel perpendicular place in body plane plot point ONE place quantities radian radical axis radius requires moving scale segment Simultaneous Equations Sines sinh slide rule Solution specific gravity spherical SQUARE ROOTS straight line subtracting table gives tangent tanh triangle TRIGONOMETRIC FUNCTIONS unit variable vector VN N VN Volume x-axis y₁ zero