If x ϵ R and m = x 2 ( x 4 − 2 x 2 + 4 ) , then m lies in the interval Options: A . &nbsp[0,14] B . &nbsp[0,13] C . &nbsp[0,12] D . &nbsp[0,15]

Answer: Option C : C m = x 2 ( x 2 − 1 ) 2 + 3 = + i v e i . e . ≥ 0 Again m = 1 x 2 + 4 x 2 − 2 = 1 ( x − 2 x ) 2 + 2 ≤ 1 2 m ϵ [ 0 , 1 2 ]

If xϵR and m=x2(x4−2x2+4), then m lies in the interval

Question

x ϵ R

and

m = \frac{x^{2}}{(x^{4} - 2 x^{2} + 4)}

, then m lies in the interval

Options:

A . [0,14]

B . [0,13]

C . [0,12]

D . [0,15]

Answer: Option C
:
C

m = \frac{x^{2}}{(x^{2} - 1)^{2} + 3} = + i v e i . e . \geq 0

Again

m = \frac{1}{x^{2} + \frac{4}{x^{2}} - 2} = \frac{1}{{(x - \frac{2}{x})}^{2} + 2} \leq \frac{1}{2}

m ϵ [0, \frac{1}{2}]

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