MLC WIR 20B M151 week10 #6c
Using L'Hospital's Rule to evaluate a limit representing a derivative at a point
Simplifying Difference Quotients in Python
Author: David Manuel
In this video, it is demonstrated how to simplify difference quotients in Python. It is then shown how to use Python to find the derivative of the function by substituting \(h=0\) in the simplified difference quotient.
Transcript 11
Transcript 11
Problem: Use the limit definition to find the derivative of \[f(x)=\frac{1}{x^3}\]
from sympy import *
# Use limit definition to find derivative of f(x)=1/x^3
h,x=symbols('h x')
f=1/x**3
#Step 1 command: subs
diffqt=(f.subs(x,x+h)-f)/h
print('The difference quotient is',diffqt)
#Step 2 command: factor, expand, or simplify
print(diffqt.expand().simplify())
#Step 3 command: subs
print(diffqt.expand().simplify().subs(h,0))
# Use limit definition to find derivative of f(x)=1/x^3
h,x=symbols('h x')
f=1/x**3
#Step 1 command: subs
diffqt=(f.subs(x,x+h)-f)/h
print('The difference quotient is',diffqt)
#Step 2 command: factor, expand, or simplify
print(diffqt.expand().simplify())
#Step 3 command: subs
print(diffqt.expand().simplify().subs(h,0))
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