Created
January 29, 2021 21:40
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A collection of functions for performing differential and integral calculus in Python.
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# Find the tangent of any polynomial function at x. | |
def find_tangent(x, coefficients): | |
slope = 0 | |
intercept = coefficients[0] | |
for i, coefficient in enumerate(coefficients): | |
if i != 0: | |
slope += coefficient * i * pow(x, i - 1) | |
intercept += coefficient * pow(x, i) | |
return [intercept - slope * x, slope] | |
# Find the area under any polynomial function within bounds. | |
# This function works assuming your curve is either entirely above or entirely below the x axis. | |
# If your curve crosses the x axis within the given bounds you will need to first find the roots (x intercepts) and then calculate the segments above and below the axis separately. | |
def find_area(lower_limit, upper_limit, coefficients): | |
lower = 0 | |
upper = 0 | |
for i, coefficient in enumerate(coefficients): | |
lower += (coefficient * pow(lower_limit, i + 1)) / (i + 1) | |
upper += (coefficient * pow(upper_limit, i + 1)) / (i + 1) | |
return abs(upper - lower) |
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