Question-9057

Question Number 9057 by sandipkd@ last updated on 16/Nov/16

Answered by aydnmustafa1976 last updated on 16/Nov/16

n s i n \frac{1}{n} = l i m \frac{s i n \frac{1}{n}}{\frac{1}{n}} = l i m \frac{s i n t}{t} = 1 t h e r e f o r e 4 \int_{0}^{1} \frac{1}{x^{2} + 1} d x = 4 . a r c t g x ∣_{0}^{1} = 4 (\frac{Π}{4} - 0) = Π

Commented by sandipkd@ last updated on 17/Nov/16

t h a n k s . . i w a s c o n f u s e d i n n \sin 1 / n

Answered by aydnmustafa1976 last updated on 17/Nov/16

l i m \underset{n \to \infty}{} \int_{0}^{n s i n \frac{1}{n}} \dots . . = \int_{0}^{l i m \frac{1}{\frac{1}{n}} . s i n \frac{1}{n}} \dots . = \int_{0}^{l i m \frac{s i n \frac{1}{n}}{\frac{1}{n}}} \dots = \dots .

Answered by aydnmustafa1976 last updated on 17/Nov/16

n o t e : l i \underset{n \to \infty}{m} \frac{s i n \frac{1}{n}}{\frac{1}{n}} = l \underset{\frac{1}{n} \to 0}{i m} \frac{s i n \frac{1}{n}}{\frac{1}{n}} = l i \underset{t \to 0}{m} \frac{s i n t}{t} = 0

Answered by aydnmustafa1976 last updated on 17/Nov/16

s o r r y l i m \frac{s i n t}{t} = 1 w h e n t \to 0