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The value of lim(xrarr0) (sin(sinx)-tan(...

The value of `lim_(xrarr0) (sin(sinx)-tan(sinx))/(sin^3(sinx))`, is

A

`(1)/(2)`

B

`-1`

C

`(1)/(2)`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that `lim_(xto0) (tanx-sin)/(sin^3x)=(1)/(2)`,
`therefore lim_(xto0) (sin(sinx)-tan(sinx))/(sin^3(sinx))`
`=-lim_(xto0) (tan(sinx)-sin(sinx))/(sin^3(sinx))=(1)/(2)`
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Section I - Solved Mcqs
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  4. The value of lim(xrarr oo) x{(1)/(e)-((x)/(x+1))^x} , is

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  6. If the equation of the normal to the curve y=f(x) at x=0 is 3x-y+3=0 t...

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  10. Let f(x)=(loge(x^2+e^x))/(loge(x^4+e^2x)). If lim(xrarr oo) f(x)=l and...

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  11. lim(nto oo) ((nsqrt(p)+nsqrt(q))/(2))^n,p,q,gt 0 equals

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  12. The value of lim(xrarr0)(e^(x)-cos2x-x)/(x^2) , is

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  13. lim(xrarr0) (2^(|x|)e^(|x|)-|x|log(2)2-1)/(xtanx) is equal to

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  14. If("lim")(xvecoo)(n .3^n)/(n(x-2)^n+n .3^(n+1)-3^n)=1/3, t h e n t h e...

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  15. The value of lim(x to oo)(2x^(1//2)+3x^(1//3)+4x^(1//4)+…………+nx^(1//n)...

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  16. If A,B,C are positive real numbers such that lim(xrarr oo) (sqrt(Ax^2+...

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  17. Let kgt0 and lambda =lim(xrarr0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-x^...

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  18. If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)...

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  19. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  20. If lim(xrarroo) (8x^3+mx^2)^(1//3)-nx exists and is equal to 1 , then ...

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