Limits Continuity And Differentiability Question 102
Question: Consider the following statements:
- The function f (x) = greatest integer $ \le x,x\in R $ is a continuous function.
- All trigonometric functions are continuous on R. Which of the statements given above is/are correct?
Options:
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
Correct Answer: D
Solution:
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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