If-t-denotes-the-integral-part-of-t-then-lim-x-1-x-sin-pix-A-equals-1-B-equals-1-C-equals-0-D-does-not-exist-

Question Number 186758 by EnterUsername last updated on 09/Feb/23

If [t] denotes the integral part of t, then \lim_{x \to 1} [x \sin π x]

(A) equals 1 (B) equals - 1

(C) equals 0 (D) does not exist

Answered by Gazella thomsonii last updated on 10/Feb/23

\lim_{x \to 1} \int x \sin (π x) d x = \lim_{x \to 1} {(\frac{1}{π})}^{2} \cdot (\sin (π x) - π x \cos (π x)

\frac{1}{π^{2}} (D) \cdot \cdot \cdot \cdot {Dosen}^{'} t Exist

Answered by mr W last updated on 10/Feb/23

\lim_{x \to 1^{-}} [x \sin π x] = 0

\lim_{x \to 1^{+}} [x \sin π x] = - 1

\Rightarrow \lim_{x \to 1} [x \sin π x] {d o e s n}^{'} t e x i s t!

Commented by EnterUsername last updated on 10/Feb/23

Thank you, Sir.