Elements of Differential Calculus for Mathematics, Physics and Engineering Students |
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Page 83
... interval St. We can say that the smaller this time interval , the closer will be the assessment of its velocity at the instant t . If we denote the instantaneous velocity of P at time t by v ( t ) , it is clear that | Ss / St — v ( t ) ...
... interval St. We can say that the smaller this time interval , the closer will be the assessment of its velocity at the instant t . If we denote the instantaneous velocity of P at time t by v ( t ) , it is clear that | Ss / St — v ( t ) ...
Page 164
... interval a≤x≤b and let f ( x ) be differentiable twice within this interval . Let f ( a ) and f ( b ) have opposite signs and let us assume that f ' ( x ) and ƒ " ( x ) retain the same sign throughout the interval and that they do not ...
... interval a≤x≤b and let f ( x ) be differentiable twice within this interval . Let f ( a ) and f ( b ) have opposite signs and let us assume that f ' ( x ) and ƒ " ( x ) retain the same sign throughout the interval and that they do not ...
Page 168
... interval [ a , b ] , then the function f ( x ) is constant within that interval . If x and x2 ( x1 < x2 ) are any two arbitrary interior points of the interval [ a , b ] , then by mean value theorem But f ' ( t ) = ƒ ( x2 ) = f ( x1 ) + ...
... interval [ a , b ] , then the function f ( x ) is constant within that interval . If x and x2 ( x1 < x2 ) are any two arbitrary interior points of the interval [ a , b ] , then by mean value theorem But f ' ( t ) = ƒ ( x2 ) = f ( x1 ) + ...
Contents
INTRODUCTION | 1 |
SETS FUNCTIONS RELATIONS AND GRAPHS | 3 |
THEIR LIMITS AND CONVERGENCE | 26 |
Copyright | |
13 other sections not shown
Common terms and phrases
angle approximation asymptote axis cartesian circle cone Consider constant continuous coordinates corresponding cos² cos³ cosec cosh decreasing denote derivative differentiable divergent dx dy dy dx dy/dx elements ellipse f(p+h following curves ft./sec function given hyperbola independent variables intersect interval limit loge mean value theorem minimum monotonic monotonic decreasing neighbourhood origin parabola particle pedal equation plane point of inflexion polar equation positive pedal prove radius of curvature real numbers relative maximum respect Rolle's theorem satisfied sec² sequence set of points Similarly simple harmonic motion sin² sin³ sinh straight line subtangent surface surface of revolution tangent tanh u-series is convergent values velocity x²+y² y₁ zero ди ди дх ду