Consider the following statements :

I. f(x) is continuous at x = 0.

Il. f(x) is continuous at x = 1

Which of the statements given above is/are correct?

Question

Question

Direction : Consider the following for the items that follow :

Let f(x) = |x|² - |x²|

This question was previously asked in

NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)

Answer 1

Explanation:

f(x) = [x]²– [x²]

At x = 0

LHL = \(\rm \lim_h\rightarrow 0\) [0 – h]² – [(0 – h)²]

= (–1)² – 0 = 1

RHL = \(\rm \lim_h\rightarrow0 [0 + h]^2 – [(0 + h)^2] \)

= 0 – 0 = 0

LHL ≠ RHL; f(x) is not continuous at x = 0

At x = 1

LHL = \(\rm \lim_h\rightarrow 0\) [[1 – h]² – [(1 – h)²]

= 1 – 1 = 0

RHL = \(\rm \lim_h\rightarrow 0\) [1 + h]² – [(1 + h)²]

= 1 – 1 = 0

⇒ f(x) is continuous at x = 1; LHL = RHL.

∴ Option (b) is correct.

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