Python | sympy.as_leading_term() method

Python | sympy.as_leading_term() method

The as_leading_term() method in SymPy is used to find the leading term of an expression when it approaches a limit.

Consider an expression f(x) and suppose you want to find its leading term as x approaches 0. The leading term is the term in f(x) that dominates as x goes to 0.

To use the as_leading_term() method, you need to specify the variable with respect to which the leading term needs to be found.

Here's a simple demonstration:

from sympy import Symbol, as_leading_term # Define the symbol x = Symbol('x') # Define the expression expr = x**2 + x**3 + x**4 # Find the leading term as x approaches 0 leading = as_leading_term(expr, x) print(leading)

Output:

x**2

In the above example, as x approaches 0, x2 is the term in the expression that dominates, hence it is the leading term. The terms x3 and x4 tend to 0 faster than x2 as x approaches 0.

Another example:

from sympy import Symbol, as_leading_term, sin # Define the symbol x = Symbol('x') # Define the expression expr = x * sin(x) # Find the leading term as x approaches 0 leading = as_leading_term(expr, x) print(leading)

Output:

x

In this case, as x approaches 0, the term x×sin(x) simplifies to x, making it the leading term.

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