MHT CET202210 Aug 2022Evening ShiftMathematicsLimitsActual
If f(x)=[x]- [ x 4 ], x R Where [x] denotes the greatest integer less than or equal to x , then
Options
- A_ x 4⁻ f(x) exists, but _ x 4⁺ f(x) does not exist.
- Bf(x) is continuous at x=4 .
- C_ x 4⁺ f(x) exists, but _ x 4⁻ f(x) does not exist.
- DBoth _ x 4⁻ f(x) and _ x 4⁺ f(x) exist, but are not equal.
Correct answer
B. f(x) is continuous at x=4 .
Step-by-step solution
aligned & _ x 4⁻ f(x)= [4⁻ ]- [ 4⁻ 4 ]=3-0=3 and & _ x 4⁺ f(x)= [4⁺ ]- [ 4⁺ 4 ]=4-1=3 & f(4)=[4]- [ 4 4 ]=4-1=3 & _ x 4⁻ f(x)= _ x 4⁺ f(x)=f(4) & f(x) ; continuous at x=4 aligned