InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Prove that \(\lim\limits_{x \to a^+}\) [x] = [a] for all a ∈ R. Also, prove that \(\lim\limits_{x \to 1^-}\)[x] = 0lim [x], x ∈ a+ = [a] |
|
Answer» To Prove : lim [x], x ∈ a+ = [a] L.H.S = \(\lim\limits_{x \to a^+}\) [x] = \(\lim\limits_{h \to 0}\)[a+h] = [a] (Since, [a + h] = [a]) Hence, Proved. Also, To prove : \(\lim\limits_{x \to 1^-}\) [x] = 0 L.H.S = \(\lim\limits_{x \to 1^-}\) [x] = \(\lim\limits_{h \to 0}\) [1-h] = 0 (Since, [1 – h] = 0) Hence, Proved. |
|