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NDA2011MathematicsContinuity and DifferentiabilityActual

What is the value of k for which the following function f(x) is continuous for all x ? f(x)= array cc x^3-3 x+2 (x-1)^2 & for x 1 k & for x=1 array .

Options

  1. A3
  2. B2
  3. C1
  4. D-1

Correct answer

A. 3

Step-by-step solution

Since the given function is continuous so that f(1+h)=f(1-h)=f(h) Now f(1+h)=lt_ h 1 (1+h)^3-3(1+h)+2 (1+h-1)^2 lt _ h 0 1+h^3+3 h^2+3 h-3-3 h+2 (h)^2 f(x)=3 .

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