Some modern calculators allow division by zero in special cases, where it will be useful to students and, presumably, understood in context by mathematicians. Some calculators, the online Desmos calculator is one example, allow arctangent(1/0). Students are often taught that the inverse cotangent function, arccotangent, should be calculated by taking the arctangent of the reciprocal, and so a calculator may allow arctangent(1/0), giving the output formula_45, which is the correct value of arccotangent 0. The mathematical justification is that the limit as x goes to zero of arctangent 1/x is formula_45.