Find Limit Calculator

Use ^ for powers and the usual function names. Angles are in radians.
A number, a constant expression such as pi/2, or "inf" / "-inf".
Limit
1
Limit Calculator
Limit as a number
1
Notation
lim x→0 of sin(x) / x
The limit exists
yes
Limit from the left
0.9999999999999983
Limit from the right
0.9999999999999983
Indeterminate form met
0/0
How it was found
exact: L'Hôpital's rule
Worked out from OpenStax, Calculus Volume 1, chapter 2 (Limits) and section 4.8 (L'Hôpital's Rule) and 1 other source.

How this is worked out

4 steps
  1. f(x) = sin(x) / x
  2. Round 1: the quotient is in 0/0 form, so by L'Hôpital's rule differentiate top and bottom separately: cos(x).
  3. Substituting x = 0 now gives 1.
  4. Numeric check: at x = -1e-7 the value is 0.9999999999999983, which agrees.

Results are general information, not financial, tax, legal, medical or engineering advice.