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("lim")(x->0)(sin(x^2))/(1n(cos(2x^2-x))...

`("lim")_(x->0)(sin(x^2))/(1n(cos(2x^2-x)))` is equal to (a) `2 `(b) `-2` (c) `1` (d) `-1`

A

`e^(a)`

B

`-a`

C

`e^(1-a)`

D

`e^(1+a)`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xto0)lim(sin(x^(2)))/("ln"(cos(2x^(2)-x)))`
`=underset(xto0)lim(sin(x^(2)))/(log(1-2sin^(2)((2x^(2)-x)/(2))))`
`=underset(xto0)lim(sin(x^(2))x^(2))/((x^(2)log(1-2sin^(2)((2x^(2)-x)/(2))))/(-2sin^(2)((2x^(2)-x)/(2)))[-2sin^(2)((2x^(2)-x)/(2))])`
`=underset(xto0)lim-(x^(2))/((2sin^(2)((2x^(2)-x)/(2)))/(((2x^(2)-x)/(2))^(2))((2x^(2)-x)/(2))^(2))`
`=underset(xto0)lim-(2x^(2))/((2x^(2)-x)^(2))=underset(xto0)lim-(2)/((2x-1)^(2))=-2`
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CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
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  3. ("lim")(x->0)(sin(x^2))/(1n(cos(2x^2-x))) is equal to (a) 2 (b) -2 ...

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

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

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

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

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

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

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

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

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  12. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then

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  13. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  14. ("lim")(x -> 0)((1+tanx)/(1+sinx))^(cos e cx) is equal to (a)e ...

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  15. The value of lim(x->1)(2-x)^(tan((pix)/2)) is (a)e^(-2/pi) (b) e^...

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  16. The value of ("lim")(xvecoo)(cos"x"/"m")^("m") is 1 (b) e (c) e^(-1...

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  17. ("lim")(xvecoo)((n^2)/(n^2))^(n(n-1)i se q u a lto e (b) e^2 (c) e^(...

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  18. lim(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ) is ...

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  19. lim(xtooo) [((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x) is :

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  20. The value of lim(xrarr0)(1^x+2^x+3^x+...+n^x)^(a//x)/n, is:

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