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Let f(x)=lim(ntooo) (x)/(x^(2n)+1). Then...

Let `f(x)=lim_(ntooo) (x)/(x^(2n)+1).` Then

A

real and equal roots

B

complex roots

C

unequal positive real roots

D

unequal roots

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`f(x)=underset(xtooo)lim(x)/(x^(2n)+1)={{:(x", "x^(2)lt1),(0", "x^(2)gt1),(1//2", "x=1),(-1//2","x=-1):}`
`:.f(1^(+))=f(-1^(-))=0`
f(1^(-))=1,f(-1^(+))=-1`
`f(1)=1//2`
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CENGAGE-LIMITS-Exercise (Multiple)
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  10. Let L=lim(xtoa) (|2sinx-1|)/(2sinx-1). Then

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  11. Let f(x)=lim(ntooo) (x)/(x^(2n)+1). Then

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  13. Given a real valued function f such that f(x)={tan^2[x]/(x^2-[x]^2) ,...

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  14. If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be c...

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  15. The value of lim(ntooo) (1)/(1+nsin^(2)nx)" can be " (n inN)

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  16. Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less...

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  17. Given lim(x to 0)(f(x))/(x^(2))=2, where [.] denotes the greatest inte...

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