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AP EAMCET201823 Apr 2018Evening ShiftMathematicsContinuity and DifferentiabilityActual

If [x] denotes the greatest integer not exceeding the number x , then f(x) defined by f(x)= array ll [x], & if x < 2 [x]-1, & if x 2 array . is continuous in the interval.

Options

  1. A[1,2) (2,3)
  2. B[1,3)
  3. C(1,3)
  4. DR

Correct answer

B. [1,3)

Step-by-step solution

Given function, aligned & f(x)= aligned [x], & if x < 2 [x]-1, & if x 2 aligned . & At x=2, f(2)=1 & LHL & ( at x=2)= _ h 0 [2-h]=1 & and RHL (at x=2)= _ h 0 ([2+h]-1)=2-1=1 aligned So, f(x) is continuous at x=2 And [x] is continuous in [n, n+1), n integer. So, given function continuous in the interval [1,3) .

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