Solving Problems in Differential Calculus |
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Page 85
... x ) 2 T1 = 1 + 2x + 3x2 + xT = n ... + nx " -1 x + 2x2 + ... + ( n − 1 ) x ^ -1 + nx ( 1 - x ) T , = 1+ x + x2 + + ... Ur +1 u , = == r2 + 2r + 2 ( r + 2 ) ( r2 + 1 ) ( r2 + 2r + 2 ) ( r + 1 ) | xx as r → ∞ . So if x < 1 the series is ...
... x ) 2 T1 = 1 + 2x + 3x2 + xT = n ... + nx " -1 x + 2x2 + ... + ( n − 1 ) x ^ -1 + nx ( 1 - x ) T , = 1+ x + x2 + + ... Ur +1 u , = == r2 + 2r + 2 ( r + 2 ) ( r2 + 1 ) ( r2 + 2r + 2 ) ( r + 1 ) | xx as r → ∞ . So if x < 1 the series is ...
Page 94
... x | < 1 , its sum is ( 1 + x ) " , where the number n is not necessarily a positive integer . If then f ( x ) = ( 1 ... Ur + 1 = and so Ur + 1 = u , 1 ( r + 1 ) ! · n ( n − 1 ) . . . ( n − r ) x ′ + 1 , n - r r + 1 - | | xx as r ...
... x | < 1 , its sum is ( 1 + x ) " , where the number n is not necessarily a positive integer . If then f ( x ) = ( 1 ... Ur + 1 = and so Ur + 1 = u , 1 ( r + 1 ) ! · n ( n − 1 ) . . . ( n − r ) x ′ + 1 , n - r r + 1 - | | xx as r ...
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