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The value of lim(xto0) (1-(cosx)sqrt(cos...

The value of `lim_(xto0) (1-(cosx)sqrt(cos2x))/(x^(2))` is

A

`(1)/(3)`

B

`(1)/(2)`

C

`(1)/(6)`

D

`(5)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(xto0)lim(1-cosxsqrt(cos2x))/(x^(2))`
`underset(xto0)lim(1-cosxsqrt(cos2x")")(1+cosxsqrt(cos2x)))/(x^(2)"("1+cosxsqrt(cos2x")"))`
`=underset(xto0)lim(1-cos^(2)x(cos2x))/(2x^(2))`
`=underset(xto0)lim(1-cos^(2)x(2cos^(2)-1))/(2x^(2))`
`=underset(xto0)lim((1-cos^(2)x)(1+2cos^(2)x))/(2x^(2))`
`=underset(xto0)lim(sin^(2)x.(1+2cos^(2)x))/(2x^(2))`
`=(3)/(2)`
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CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. The value of ("lim")(x->a)sqrt(a^2-x^2)cot(pi/2sqrt((a-x)/(a+x))) is (...

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

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

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

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  5. The value of lim(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is (a)4 (b) ...

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

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

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

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

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

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

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

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

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

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

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  16. ("lim")(xto1)(n x^(n+1)-(n+1)x^n+1)/((e^x-e)sinpix),\ where \n=100 , ...

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  17. lim(x->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)=

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  18. The value of lim(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

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  19. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is (a)1/2 ...

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  20. If lim(xtoa)f(x)=1 and lim(xtoa)g(x)=oo then lim(xtoa){f(x)}^(g(x))=e^...

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