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BITSAT2015MathematicsContinuity and DifferentiabilityActual

If a function f(x) is given by f(x)= x 1+x + x (x+1)(2 x+1) + x (2 x+1)(3 x+1) + , , then at x=0, f(x)

Options

  1. Ahas no limit
  2. Bis not continuous
  3. Cis continuous but not differentiable
  4. Dis differentiable

Correct answer

B. is not continuous

Step-by-step solution

Let f(x)= x 1+x + x (x+1)(2 x+1) + x (2 x+1)(3 x+1) + = _ n _ r=1 ^ n x [(r-1) x+1](r x+1) = _ x _ r =1 ^ n [ x [( r -1) x +1] - 1 rx +1 ]= _ n [1- 1 n x+1 ]=1 For x=0, we have f(x)=0 Thus, we have f(x)= array ll 1, & x 0 0, & x=0 array . Clearly, _ x 0⁻ f ( x )= _ x 0⁺ f ( x ) f (0) So, f ( x ) is not continuous at x =0 .

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