Manipal MET2015MathematicsLimits
_ x -1 ( x^4+x^2+x+1 x^2-x+1 )^ 1- (x+1) (x+1)^2 is equal to
Options
- A1
- B2 3
- C3 2
- De^ 1 / 2
Correct answer
B. 2 3
Step-by-step solution
We observe that x^4+x^2+x+1 x^2-x+1 2 3 as x -1 But 1- (x+1) (x+1)^2 0 0 as x -1 _ x -1 ( x^4+x^2+x+1 x^2-x+1 )^ 1- (x+1) (x+1)^2 = ( 2 3 ) x^ _ x -1 1- (x+1) (x+1)^2 = ( 2 3 )^ _ x -1 2 ^2 ( x+1 2 ) 4 ( x+1 2 )^2 = ( 2 3 )^ 1 / 2