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Consider the following statements: 1. ...

Consider the following statements:
1. The function f(x) = greatest integer `lex,x""inR` is a continuous function.
2. All trigonometric functions are continuous on R.
Whict of the statements given above is/ are correct ?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
D
Here, greatest integer function [x] is discontinuous at its intergral value of x, oct x and cosec x are discontinuous at `0,pi,2pi` etc. tan x and sec x are discontinuous at
`x=(pi)/(2),(3pi)/(2),(5pi)/(2)` etc. Therefore the greatest integer function and all trigonometric function are not continuous for `x""inR`
Therefore, neither (1) nor (2) are true.
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