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Name: ____________________ Project 3 (20 Points) Math-CS-143C
Due: Tuesday, April 21, 11:59pm Spring 2020 (Dr. Saleem)
Use 10 decimal digits and a calculator or a programming language or computer package of your choice.
Project: Apply various differentiation formulas to approximate ?′(0) ?? ?(?) = √1+????
1+????
. Find the best h.
(1) Show your steps and prove that ?′(0) = √18
(2) Apply forward difference formula with 10 decimal digits to approximate ?′(0) with various values of the
step h, and fill the table. From the table below , the best h is _________________
h=step ?′(0) by forward difference Error=|exact-approximate|
h=0.1
0.001
0.00001
0.0000001
0.000000001
(3) Apply center difference formula with 10 decimal digits to approximate ?′(0) with various values
of the step h, and fill the table. From the table below, the best h is _________________
h=step ?′(0) by center difference Error=|exact-approximate|
h=0.1
0.001
0.00001
0.0000001
0.000000001
(4) Apply 5-point mid-point formula with 10 decimal digits to approximate ?′(0) with various values
of the step h, and fill the table. From the table below, the best h is _________________
h=step ?′(0) by 5-point mid-point Error=|exact-approximate|
h=0.1
0.001
0.00001
0.0000001
0.000000001
(5) Apply the book’s formula with 10 decimal digits to approximate the second derivative ?
′′(0) with various
values of the step h, and fill the table. From the table below, the best h is _________________
h=step ?
′′(0) by mid-point Error=|exact-approximate|
h=0.1
0.001
0.00001
0.0000001
0.000000001