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Defining a variable inside the function lets us control what variable we use for the limit.

For example, define tand substitute it for the variable provided by the user.

Applying this idea, we can define myfunction as follows:

def mylimit(f, x, a):
    r"""
    Return the limit of the expression `f` when `x` tends to `a`.
    """
    t = SR.var('t')
    return f.subs({x: t}).limit(t=a)

With that definition:

sage: mylimit(1/y, y, 2)
1/2

Defining a variable inside the function lets us control what variable function, we can use it for the limit.

For example, define t and substitute it for the variable provided by the user.

Applying this idea, we can define myfunction as follows:

def mylimit(f, x, a):
    r"""
    Return the limit of the expression `f` when `x` tends to `a`.
    """
    t = SR.var('t')
    return f.subs({x: t}).limit(t=a)

With that definition:

sage: mylimit(1/y, y, 2)
1/2