Solving Problems in Differential Calculus |
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Page 45
... x Fig . 27 Sketches of the graphs of sinh x , cosh x , tanh x are shown in Figs . 25 , 26 , 27 . The formal ... sech x tanh x , D sech x = D coth x = - cosech2 x . WORKED EXAMPLES 16.1 . Prove , from the definitions of §16 ELEMENTARY ...
... x Fig . 27 Sketches of the graphs of sinh x , cosh x , tanh x are shown in Figs . 25 , 26 , 27 . The formal ... sech x tanh x , D sech x = D coth x = - cosech2 x . WORKED EXAMPLES 16.1 . Prove , from the definitions of §16 ELEMENTARY ...
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... Find the stationary values of sech x + tanh x , and sketch its graph . If y dy dx = sech x + tanh x , then = -sech x tanh x + sech2 x = sech x ( sech x - tanh x ) . Since sech x is never zero , the only stationary value occurs when sech x = ...
... Find the stationary values of sech x + tanh x , and sketch its graph . If y dy dx = sech x + tanh x , then = -sech x tanh x + sech2 x = sech x ( sech x - tanh x ) . Since sech x is never zero , the only stationary value occurs when sech x = ...
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Leslie Maurice Brown. When x = 0 , y = 1. When x is large and positive , sech x is small and tanh x is near 1 , that is , y is near 1. When x is large and nega- tive , sech x is small and tanh x is near −1 , i.e. y is near — 1. When y = 0 ...
Leslie Maurice Brown. When x = 0 , y = 1. When x is large and positive , sech x is small and tanh x is near 1 , that is , y is near 1. When x is large and nega- tive , sech x is small and tanh x is near −1 , i.e. y is near — 1. When y = 0 ...
Common terms and phrases
1+x² 2x sin 3x absolutely convergent ADDITIONAL EXAMPLES angle approximately Binomial series conditionally convergent constant cos² 5x cos³ cosec cosh cosh x cosh2 coth curve d²y dx2 d²y dy d²y/dx² decimal places Deduce derivative Differentiate dt dt dx dt dx dy dx2 dx dy dx dy/dx equation feet Find the stationary finite limit harmonic series Hence hyperbolic functions increases J₁ Leibnitz's Theorem logarithm Maclaurin expansion Maclaurin series maximum minimum n²)n nt+a oscillates finitely polynomial positive integer positive terms power series power series expansion prove radians radius of convergence sec² sec³ sech series diverges series is convergent sin x sin¯¹ sin¹ sin² sin³ sinh sinh2 Sketch the graph SPDC stationary points tangent tends to infinity term in x4 u₁ velocity x-sin x+cos x²+1 y₁ Ип