Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2017MathematicsContinuity and DifferentiabilityActual

The value of f ( 0 ) , so that the function f x = 2 x - sin - 1 x 2 x + tan - 1 x is continuous at each point in its domain, is

Options

  1. A1 3
  2. B- 1 3
  3. C2 3
  4. D- 2 3

Correct answer

A. 1 3

Step-by-step solution

Since, x , sin - 1 x , tan - 1 x are continuous functions, so the function f is clearly continuous at each point of its domain except possibly at x = 0 . So, for f to be continuous at x = 0 f 0 = lim x → 0 f x = lim x → 0 2 - sin - 1 x x 2 + tan - 1 x x = 1 3 ∵ lim x → 0 sin - 1 x x = 1 , lim x → 0 tan - 1 x x = 1

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let f be the function defined by f(x)= array cc x^2-1 x^2-2|x-1|-1 , & x 1 1 2 , & x=1 array . 2024If f(x)= array cc x^2 ( x) (1+x) , & x 0 0, & x=0 array . , then at x=0, f(x) is 2024f(x)= array cc 4 & - x - 5 x^2-1 & - 5 x 5 4 & 5 x array . If k is the number of points where f(x) is not differentiable then k-2= 2024Let f be the function defined by f(x)= array ll x²-1 x²-2|x-1|-1 , & x 1 1 / 2, & x=1 array . 2020Let f x = x p sin 1 x , x ≠ 0 0 , x = 0 then f x is continuous but not differentiable at x = 0 , if 2018If f x = e x , x ≤ 0 1 - x , x > 0 , then 2017Consider the greatest integer function, defined by f ( x ) = [ x ] , 0 ≤ x < 2 . Then 2017The number of points at which the function f ( x )= 1 | x | is discontinuous is: 2016 Full Continuity and Differentiability list All BITSAT PYQs