Most Important Selected Qs for JEE AdvancedMathematicsInverse Trigonometric Functions

Let a be a positive integer such that the limit _ x 1 ( 1 x-1 - 1 x^a-2 x+1 ) exists and is equal to b:( where b 0)

Options

A⁻¹( a) is equal to 3- .
B⁻¹( b) is equal to 3- .
C⁻¹( (a+b)) is equal to 5-2 .
D⁻¹( (a-b)) is equal to 1.

Correct answer

B. ⁻¹( b) is equal to 3- .

Step-by-step solution

b= _ x 1 x^a-2 x+1-x+1 (x-1) (x^a-2 x+1 ) = _ x 1 x^a-3 x+2 (x-1) (x^a+1-2 x ) ; x=1+hb= _ h 0 (1+h)^a-3(1+h)+2 h [(1+h)^a+1-2(1+h) ] = _ h 0 (1+a h+ .)-3 h-1 h[1+a h .1-2 h] = _ h 0 (a-3) h+ a(a-1) 2 h^2 (a-2) h^2+ . a=3 and b=3 a+b=6

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