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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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  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")(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to ...

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  5. The value of ("lim")(xvec0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] ...

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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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  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")(xvec1^-)(1-sqrt(x))/((ccos^(-1)x)^2) is 4 (b) ...

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  11. ("lim")(xvecpi/2)(sin(xcosx)/("cos"(xsinx)i se q u a lto 0 (b) p/2 (...

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  12. ("lim")(xvec0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the ...

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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(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to ...

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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")(xvecoo)((2^x^n)^1//e^x-(3^x^n)^1//e^x)/(x^n) (whe...

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  17. ("lim")(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c)...

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  18. ("lim")(xvecoo)(e^1//x^2-1)/(2tan^(-1)(x^2)-pi)i se q u a lto 1 (b) -...

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  19. ("lim")(xto0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/x is equal t o (a) 2(1/(m2...

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

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