Solving Problems in Differential Calculus |
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Page 83
... terms of u is convergent for all u , then the series for y in terms of x is convergent if | x | < R2 . Identity . If ... x4∞r = 1 r = 1 x → ∞ Express u , ( x ) in partial fractions , obtaining x r - 1 ( x + r ) ( x + r − 1 ) x + r x ...
... terms of u is convergent for all u , then the series for y in terms of x is convergent if | x | < R2 . Identity . If ... x4∞r = 1 r = 1 x → ∞ Express u , ( x ) in partial fractions , obtaining x r - 1 ( x + r ) ( x + r − 1 ) x + r x ...
Page 107
... term . 21.26 . O is the middle point of the side AB of a triangle ABC . ос a , AB = 2x , angle AOC = = a . If x / a ... x4 , the power series expansion of y = log ( 1 + sin x ) . Find the Maclaurin expansion of y , as far as the same term ...
... term . 21.26 . O is the middle point of the side AB of a triangle ABC . ос a , AB = 2x , angle AOC = = a . If x / a ... x4 , the power series expansion of y = log ( 1 + sin x ) . Find the Maclaurin expansion of y , as far as the same term ...
Page 108
Leslie Maurice Brown. 21.33 . Find , as far as the term in x4 , the power series expansion of cos log ( 1 + x ) . 21.34 . Show that ecos x e ( 1-4x2 + ¿ x2 + . . . ) . = tan x -x 21.35 . Find the limit , as x → 0 , of x - sin x 21.36 ...
Leslie Maurice Brown. 21.33 . Find , as far as the term in x4 , the power series expansion of cos log ( 1 + x ) . 21.34 . Show that ecos x e ( 1-4x2 + ¿ x2 + . . . ) . = tan x -x 21.35 . Find the limit , as x → 0 , of x - sin x 21.36 ...
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