Question

2. Let y = sin (0.5?x/x). Here, x is in radian. a.) Calculate the first order derivatives at x=1, for the specified step sizes such as 0.1, 0.05 and 0.025 using Central Divided Difference Method i. incorporates two terms of the Taylor series expansion ii. incorporates more terms of the Taylor series expansion b.) Calculate the second order derivatives at x=1, for the specified step sizes such as 0.1, 0.05 and 0.025 using Central Divided Difference Method i. incorporates two terms of the Taylor series expansion ii. incorporates more terms of the Taylor series expansion c.) Write matlab m-files which implement the Central Divided Difference Method incorporating more terms of the Taylor series expansion to calculate i. the first order derivative and ii. second order derivatives. Perform your calculations for the specified step sizes such as 0.1, 0.05 and 0.025. Show your result in a table in the command window by giving step size(?x), Approximate value(Av) and Etp:Percent True error.

          2. Let y = sin (0.5?x/x). Here, x is in radian.
a.) Calculate the first order derivatives at x=1, for the specified step sizes such
as 0.1, 0.05 and 0.025 using Central Divided Difference Method
i.
incorporates two terms of the Taylor series expansion
ii.
incorporates more terms of the Taylor series expansion
b.) Calculate the second order derivatives at x=1, for the specified step sizes
such as 0.1, 0.05 and 0.025 using Central Divided Difference Method
i.
incorporates two terms of the Taylor series expansion
ii.
incorporates more terms of the Taylor series expansion
c.) Write matlab m-files which implement the Central Divided Difference
Method incorporating more terms of the Taylor series expansion to
calculate
i.
the first order derivative and
ii. second order derivatives.
Perform your calculations for the specified step sizes such as
0.1, 0.05 and 0.025. Show your result in a table in the command
window by giving step size(?x), Approximate value(Av) and
Etp:Percent True error.

2. Let y = sin (0.5?x/x). Here, x is in radian.
a.) Calculate the first order derivatives at x=1, for the specified step sizes such
as 0.1, 0.05 and 0.025 using Central Divided Difference Method
i.
incorporates two terms of the Taylor series expansion
ii.
incorporates more terms of the Taylor series expansion
b.) Calculate the second order derivatives at x=1, for the specified step sizes
such as 0.1, 0.05 and 0.025 using Central Divided Difference Method
i.
incorporates two terms of the Taylor series expansion
ii.
incorporates more terms of the Taylor series expansion
c.) Write matlab m-files which implement the Central Divided Difference
Method incorporating more terms of the Taylor series expansion to
calculate
i.
the first order derivative and
ii. second order derivatives.
Perform your calculations for the specified step sizes such as
0.1, 0.05 and 0.025. Show your result in a table in the command
window by giving step size(?x), Approximate value(Av) and
Etp:Percent True error.

Added by Holly T.

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