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lim(xto-1)((x^4+x^2+x+1)/(x^2-x+1))^((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) `(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 PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  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 equal...

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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(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repre...

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

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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(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is (a)4 (b) ...

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  11. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

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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->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x ...

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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->0)(sin(x^2))/(1n(cos(2x^2-x))) is equal to (a) 2 (b) -2 ...

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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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