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("lim")(xvec1)((x^4+x^2+x+1)/(x^2-x+1))^...

`("lim")_(xvec1)((x^4+x^2+x+1)/(x^2-x+1))^(1-"cos"(x+1))/((x+1)^(2))i se q u a lto` `1` (b) `(2/3)^(1/2)` (c) `(3/2)^(1/2)` (d) `e^(1/2)`

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 ENGLISH-LIMITS-Exercises (Single Correct Answer Type)
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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")(xvec1^-)(1-sqrt(x))/((ccos^(-1)x)^2) is 4 (b) ...

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

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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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