MCQ
$\lim_\limits{\text{x} \rightarrow 1}{1−\text{x}+[\text{x}+1]+[1−\text{x}]}$, where [x] denotes greatest integer function, is
- A0
- B1
- C-1
- D2
$\lim_\limits{\text{x} \rightarrow 1}{1−\text{x}+[\text{x}+1]+[1−\text{x}]}$, where [x] denotes greatest integer function, is
Solution:
Substitute x = 1 + t
$ \text{L.H.S} \lim_\limits{\text{t}\rightarrow o^{-}} (-\text{t}+[2+\text{t}]+[-\text{t}])$
= 0 + 1 + 0 = 1
$ \text{R.H.S} \lim_\limits{\text{t}\rightarrow o^{-}} (-\text{t}+[2+\text{t}]+[-\text{t}])$
= 0 + 2 - 1 = 1
L.H.S = R.H.S
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
The inclination of the line x - y + 3 = 0 with the positive direction of x-axis is:
Two dice are thrown simultaneously. Find the probability of getting an even number as the sum.
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is.