Which of the following functions is not continuous at the origin?

  1. sin x
  2. x
  3. x sin x

Answer (Detailed Solution Below)

Option 4 :

Detailed Solution

Download Solution PDF

Concept:

  • A function is said to continuous at a given value if the function does not have a sudden change at that value.
  • If two functions are individually continuous then it’s summation difference, the product will be also continuous.
  • A function is continuous at x = a
    If L.H.L = R.H.L = f(a)
    i.e.  
  • If f(x) and g(x) are individually continuous then it’s f(x) ± g(x), f(x) ⋅ g(x) and  will be continuous.

Calculation:

Option (A):

Let f(x) = sin x

From graph, at origin i.e. x = 0, sin x is continuous.

Option (B):

Let g(x) = x

From graph at origin i.e. x = 0

g(x) = x is continuous.

Option (C):

Let h(x) = x sin x

h(x) = g(x) ⋅ f(x)

Since f(x) and g(x) is individually continuous at origin, so h(x) will be also continuous.

Option (D):

Let  

Since sin x is continuous at origin and x is also continuous at origin and values are zero.

i.e.  

At origin:

  is a indeterminate form)

Therefore, we can say that.

h(x) will be discontinuous at origin as at x = 0, h(x) become undefined.

So, option (D) is correct as  is discontinuous at origin.

Latest BPSC Lecturer Updates

Last updated on May 9, 2025

-> The BPSC Lecturere DV will be held on 28th May 2025.

-> The written exam took place on 20th March 2025.

-> BPSC Lecturer notification was released for 6 vacancies.

-> The BPSC recruits eligible candidates for the post of Lecturer for various disciplines in Government Colleges across the state.

-> Candidates must attempt the BPSC Lecturer EC Mock Tests. Candidates can also download and practice from the BPSC Lecturer previous year papers

Hot Links: teen patti party teen patti vungo real teen patti teen patti bodhi