Function f(x) = \[x] cos (f(x) = x^{2}); \[.] is GIF, is dis... | MATH - CONTINUITY | SolveeIt | Solveeit

Today, August 24

Question

Function f(x) = [x] cos $f(x) = x^{2}$ ; [.] is GIF, is discontinuous at

A

∀ x ∈ R

B

x ∈ I

C

x ∉ I

D

None of these

Answer

None of these

Explanation

Solution

At x = n ∈ I LHL. $\lim _ { h \rightarrow 0 }$ [n – h] cos (2(n–h)–1)π/2

⇒ (n–1)cos(2n–1/2)π =0, RHL. $\lim _ { h \rightarrow 0 }$

[n + h]cos(2(n+h)–1/2)π

= n. cos (2n – 1/2)π = 0 f(n) = [n].

cos (2n–1/2)π = 0 so continuous ∀ x ∈ R.