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All answers must be typed or handwritten in the spaces provided. SUBMIT the PDF version to CANVAS .
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 𝑓′(0) 𝑖𝑓 𝑓(𝑥) = √1+𝑠𝑖𝑛𝑥
1+𝑐𝑜𝑠𝑥
. Find the best h.
(1) Show your steps and prove that 𝑓′(0) = √18
. Call it “exact answer”. Show your work below.
(2) Apply forward difference formula with 10 decimal digits to approximate 𝑓′(0) with various values of the
step h, and fill the table. From the table below , the best h is _________________
h=step 𝑓′(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 𝑓′(0) with various values
of the step h, and fill the table. From the table below, the best h is _________________
h=step 𝑓′(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 𝑓′(0) with various values
of the step h, and fill the table. From the table below, the best h is _________________
h=step 𝑓′(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 𝑓
′′(0) with various
values of the step h, and fill the table. From the table below, the best h is _________________
h=step 𝑓
′′(0) by mid-point Error=|exact-approximate|
h=0.1
0.001
0.00001
0.0000001
0.000000001

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