Question

The condition for removal discontinuity is ____________

(a) Left hand limit = right hand limit ≠ function value

(b) Left hand limit ≠ right hand limit = function value

(c) Right hand limit ≠ left hand limit = function value

(d) Left hand limit ≠ right hand limit ≠ function value

The question was posed to me during an internship interview.

Question is from Limits in portion Beyond the Basics of MATLAB

Answer 1

Right choice is (a) Left hand limit = right hand limit ≠ function value

The best explanation: The condition of removal discontinuity is given by option Left hand limit = right hand limit ≠ function value only. Rest are incorrect because the two conditions of removal discontinuity is limn→n0 f(n) < ∞  and f(n0) < ∞. So the function should have equal values while reaching the limiting value from both directions and it should have a finite value at the limiting value. But since there is a discontinuity at the limiting value, the values after approaching the function from both directions is not equal to the function value at the limiting value.