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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let f(x)= array ll ^3 x+ ^2 x-a x-a e^ ( ian x-2) -1 , & x (0, / 2)-x₀ b, & x x₀ array . . If f is continuous in (0, / 2) then find the value of [a+b+x₀ ] . [Note: [y] denotes greatest integer function less than or equal to y .]

Correct answer

17

Step-by-step solution

aligned x₀ & = ⁻¹(2) b & = _ x ⁻¹ 2 ( ^2 x-a )(1+ x) e^ ( x-2) -1 & = _ x ⁻¹ 2 ( x+ a )( x- a )(1+ x) ( x-2) aligned For the existence of limit a =2 a=4 aligned b & =12 [a+b+x₀ ] & = [4+12+ ⁻¹(2) ]=17 aligned

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