Evaluate-lim-n-n-n-1-e-1-x-dx-

Question Number 160006 by HongKing last updated on 23/Nov/21

Evaluate :

\lim_{n \to \infty} \underset{n}{\int^{n + 1}} e^{\frac{1}{x}} dx = ?

Commented by kowalsky78 last updated on 23/Nov/21

T h e a n s w e r i s 1 . I n f a c t, 1 ⩽ e^{\frac{1}{x}} ⩽ e^{\frac{1}{n}} f o r e v e r y x \in [n, n + 1] a n d e v e r y n .

I n t e g r a t i n g t h i s i n e q u a l i t y a n d t a k i n g l i m i t w e c o n c l u d e t h a t t h e a n s w e r i s 1 .

Commented by HongKing last updated on 25/Nov/21

Thank you my dear Ser