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lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1...

`lim_(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2))` is equal to

A

1

B

-1

C

`(1)/(2)`

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xto-1)lim((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^(underset(xto-1)lim(1-cos(x+1))/(x+1)^(2))`
`=((2)/(3))^(underset(xto-1)lim("sin"^(2)((x+1)/(2)))/(2((x+1)/(2))^(2)))`
`=((2)/(3))^((1)/(2))`
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CENGAGE-LIMITS-Exercise (Single)
  1. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  2. lim(ntooo) sum(x=1)^(20)cos^(2n)(x-10) is equal to

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  3. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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  4. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  5. The value of lim(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] rep...

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  6. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

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  7. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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  8. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

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  9. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

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  10. The value of lim(xto1^(-)) (1-sqrt(x))/((cos^(-1)x)^(2)) is

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  11. lim(xto pi//2) (sin(xcosx))/(cos(xsinx)) is equal to

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  12. lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greates...

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  13. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  14. If f(x)=lim(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal...

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  15. lim(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part o...

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  16. The value of lim(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x))...

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  17. lim(x to 0) (sin(x^(2)))/("ln"(cos(2x^(2)-x))) is equal to

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  18. lim(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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  19. lim(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

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  20. The value of lim(ntooo) [(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...+(e^...

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