How it works
This page evaluates selected standard limits. A polynomial is continuous, so its limit is found by direct substitution. The reciprocal is undefined at zero, while lim sin(x)/x as x approaches zero equals 1 in radians.
Standard formula
lim f(x) as x approaches aWorked example
For x² + 2x + 1 as x approaches 3, substitute 3 to get 16.
Frequently Asked Questions
Why is sin(x)/x equal to 1 at zero?
It is a standard trigonometric limit when x is measured in radians.
What happens to 1/x at zero?
The two-sided limit does not exist because the function diverges with opposite signs.
Can this solve every limit?
No. It focuses on a few common forms and shows their assumptions explicitly.
Are angles in degrees?
The sin(x)/x identity uses radians.