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In Progress... |

In Progress... |

f (x) = 1( + x) .

ii) Use the polynomial in part (i) to approximate 1.1 and find a bound for the

error involved.

iii) Use the polynomial in part (i) to approximate ∫

+

1.0

0

/1 2

1( x) dx .

In Progress... |

length of the graph

x

y

1

= between the points )1,1( and

5

1

,5

x 1 2 3 4 5

4

4

1

x

+ x

1.414 1.031 1.007 1.002 1.001

In Progress... |

x

u c e c e

α −α

= 1 + 2

is a solution of the difference equation

2 cosh 0 ux+1 − ux α + ux−1 =

In Progress... |

1 y′ = 2xy, y )1( = at x = 5.1 with h = 1.0

If the exact solution is 1

2

( )

−

=

x

y x e , find the error.

In Progress... |

∫

+

=

1

0

2

1

1

x

dx

by using the trapezoidal rule with 125 h = ,5.0 25.0 , .0 . Improve this value by using

the Romberg’s method. Compare your result with the true value.

In Progress... |

4 O h calculate approximate solution of the IVP,

y′ = 1− x + 4y, y )0( = 1 at x = 6.0 , taking h = 1.0 and 2.0 . Use extrapolation

technique to improve the accuracy.

In Progress... |

x

f x

+

=

1

1

( ) in

the interval ]4,1[ with equal step length. Determine the spacing h such that

quadratic interpolation gives result with accuracy 6

1 10−

× .

In Progress... |

2

1 1

2

2 2 δ

+ µ δ = + where µ and δ are the average and central

differences operators, respectively

In Progress... |