| 1. The function f (x) = greatest integer \[\le x,\text{ }x\in R\]is a continuous function. |
| 2. All trigonometric functions are continuous on R. |
| Which of the statements given above is/are correct? |
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Correct Answer: D
Solution :
[d] Here, greatest integer function [x] is discontinuous at its integral value of x, cot x and cosec x are discontinuous at \[0,\pi ,2\pi \] etc. and tan x and sec x are discontinuous at \[x=\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2}\] etc. therefore the greatest integer function and all trigonometric functions are not continuous for \[x\in R\] Therefore, neither (1) nor (2) are true.
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