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Most Important Selected Qs for JEE AdvancedMathematicsLimits

Let f(x)= _ n (a^ 1 n + b+ x n )^n where a, b>0 be a non-constant function and L= _ x 0 f(x)-a 1- x . Identify which of the following statement(s) is(are) correct?

Options

  1. AThe number of solution(s) of the equation f(x)=|x| are 3 .
  2. BThe number of solution(s) of the equation f(x)=|x| are 2 .
  3. Ca+L=0
  4. Da+L+3 b e=2

Correct answer

C. a+L=0

Step-by-step solution

f(x)= _ n (a^ 1 n + b+ x n )^n, b=-1 b=e⁻¹ aligned & =e^ _ n ( a^ 1 n -1 1 n - (1- x n ) 1 n ) =e^ a- x^2 2 =a e^ -x^2 2 & f(x)=|x| a e^ -x^2 2 =|x| & L= _ x 0 a e^ -x^2 2 -a ( 1- x x^2 ) x^2 =-a & L+a=0 and L+a+3 b e=3 aligned

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