Sun	Mon	Tue	Wed	Thu	Fri	Sat
27	28	29	30	1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31
1	2	3	4	5	6	7

Back to Main Page

Multiple Choice Questions

Consider the following statements in respect of the function y x x isin 1 1 where is ...........

Mathematics (NDA) limits

Consider the following statements in respect of the function y = [x], x∈(-1, 1) where [.] is the greatest integer function :

1. Its derivative is 0 at x = 0.5

2. It is continuous at x = 0

Which of the above statements is/are correct?

This questions was previously asked in

2022 NDA -1 Math

View All NDA Previous Year Papers

1 only

2 only

Both 1 and 2

Neither 1 nor 2

छोटे Courses बड़े Results

Master limits

Prepare through Micro-courses

Try Now

Explanation:

- Statement 1: The greatest integer function, also known as the floor function $[x]$ , is not differentiable at any integer or at any point where $x$ causes a jump in the function. At $x = 0.5$ , the function steps from 0 to 1 across this point in the interval $(- 1, 1)$ , meaning it's not differentiable here. Therefore, its derivative is not 0 at $x = 0.5$ .

- Statement 2: The greatest integer function $[x]$ creates discontinuities at integer points. At $x = 0$ , there's a jump from $- 1$ to $0$ because $[x]$ equals 0 for $x = 0$ , but just before it is $- 1$ . Therefore, it's not continuous at $x = 0$ .