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The value of lim(xrarroo) x^(2)(1-cos.(2...

The value of `lim_(xrarroo) x^(2)(1-cos.(2)/(x))` is

A

0

B

`1//4`

C

`2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(xrarroo)(lim)x^(2)(1-cos.(1)/(x))`
`" "=underset(xrarroo)(lim)x^(2)xx2sin^(2)((1)/(2x))`
`" "=underset(xrarroo)(lim)(2x^(2)xxsin^(2)((1)/(2x)))/((1)/(4x^(2))xx4x^(2))`
`" "=(1)/(2)`
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CENGAGE PUBLICATION-LIMITS-Single Correct Answer Type
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  2. lim(xrarr(pi)/(2)) (1-sinx)tanx=

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  3. The value of lim(xrarroo) x^(2)(1-cos.(2)/(x)) is

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  4. lim(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

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  5. lim(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

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  6. underset(xrarroo)(lim)(sinx/x)

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  7. lim(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)}...

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  8. lim(xrarr0) (3 tan3x-4 tan2x-tanx)/(4x^(2)tanx)

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  9. underset(xrarr1)(lim)(2/(1-x^2)+1/(x-1))

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  10. The value of lim(xrarr(pi)/(4)) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

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  11. The value of lim(xrarroo) (e^(sqrt(x^(4)+))-e^((x^(2)+1))) is

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  12. The value of lim(xrarrpi//4) (tan^(3)x-tanx)/(cos(x+(pi)/(4))) is

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  13. (lim)(xvecpi/2)((1-sin x)(8x^3-pi^3)cos x)/((pi-2x)^4) a.(pi^2)/6 b...

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  14. lim(xrarroo) (sum(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))=

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  15. If lim(xrarr0) (f(x))/(x^(2))=a and lim(xrarr0) (f(1-cosx))/(g(x)sin^(...

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  16. If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt...

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  17. If k in I such that lim(nrarroo) (cos.(kpi)/(4))^(2n)-(cos.(kpi)/(6))^...

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  18. If a(n) and b(n) are positive integers and a(n)+sqrt2b(n)=(2+sqrt2)^(n...

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  19. The value of lim(x rarr 0) ((tanx^((1)/(5)))/((tan^(-1)sqrtx)^(2))(log...

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  20. The value of lim(xrarr3) ((x^(3)+27)log(e)(x-2))/(x^(2)-9) is

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