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124 EXCEL: NUMERICAL METHODS
Problems
Answers to the following problems are found in the folder "Ch. 06 (Differentiation)"
in the "Problems & Solutions" folder on the CD.
1. Using the data file "Titration Curve", obtain the first and second derivative.
The "endpoint1' of a titration is considered to be the volume at the %flexion
point": that is, where the curve y = F(x) has maximum slope, or where the
first derivative reaches a maximum, or where the second derivative passes
through zero; the last is the easiest to determine graphically or
mathematically.
2. Using the data file "Student Potentiometric Data", obtain the first and second
derivative.
3. Using Excel's SIN function, create a table of sine, in one degree increments of
0 (remember that Excells trigonometric functions require angles in radians).
Now calculate d sine, using one of the formulas in Table 6-1. Compare your
answer with the exact: d sine = cose. Experiment with different formulas
from Table 6-1 to compare the errors.
4. Determine the first and second derivatives of the function
y=2x3 -20x2 +llx+30 overtherangex=-5 tox= 10.
5. Determine the first derivative of the function y = x2 - 1 x 1 0-6 x + 1 x 1 0-15
over the range x = 0 to x = 2 x
6. Determine the first derivative of the following functions over suitable ranges
of x:
