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Evaluate lim(x->pi/3)(sqrt(1-cos6x))/(sq...

Evaluate `lim_(x->pi/3)(sqrt(1-cos6x))/(sqrt2(pi/3-x))`

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`lim_(x->pi/3)(sqrt(1-cos6x))/(sqrt2(pi/3-x))`
`=lim_(x->pi/3)(sqrt(2sin^2 3x))/(sqrt2(pi/3-x))`
`=lim_(x->pi/3)(sqrt2sin3x)/(sqrt2(pi/3-x))`
`=lim_(x->pi/3)(sin3x)/(pi/3-x)`
`=lim_(x->pi/3)(3sin3x)/(pi-3x)`
`=lim_(x->pi/3)(3sin(pi-3x))/(pi-3x)`
`=3`
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RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: (lim)(n->oo)2^(n-1)sin(a/(2^n))

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  2. Evaluate the following limit: lim(x->pi/2)(sin2x)/(cos x)

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  3. Evaluate lim(x->pi/3)(sqrt(1-cos6x))/(sqrt2(pi/3-x))

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  4. Evaluate the following limit: lim(x->pi/4)(1-t a n x)/(x-pi/4)

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  5. Evaluate the following limit: lim(x->pi/3)(sqrt(3)-t a n x)/(pi-3x)

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  6. Evaluate the following limit: lim(x->pi//2)(sqrt(2)-sqrt(1+sin x))/(co...

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  7. Evaluate the following limit: lim(x->pi/4)(sqrt(2)-cos x-sin x)/((pi/4...

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  8. Evaluate the following limit: lim(x->a)(cos x-cos a)/(sqrt(x)-sqrt(a))

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  9. Evaluate the following limit: lim(x->a)(cossqrt(x)-cossqrt(a))/(x-a)

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  10. Evaluate the following limit: lim(x->1)(1+cospix)/((1-x)^2)

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  11. Evaluate lim(x->pi/4)(1-sin2x)/(1+cos4x)

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  12. Evaluate: (lim(n->oo)ncos(pi/(4n))sin(pi/(4n))

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  13. Evaluate the following limit: lim(n->oo)(sin(a/(2^n)))/(sin(b/(2^(n\ )...

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  14. Evaluate the following limit: lim(x->2)(x^2-x-2)/(x^2-2x+"sin"(x-2))

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  15. lim(x->1)(1-x)tan(pix)/2=

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  16. The value of lim(x->pi) (sqrt(2+cosx)-1)/(x-pi)^2

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  17. Evaluate the following limit: lim(x->1)(1-1/x)/(sinpi(x-1))

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  18. Evaluate the following limit: lim(x->pi/4)(sqrt(2)-cos x-sin x)/((4x-p...

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  19. Evaluate the following limit: lim(x->pi/4)(cos x-sin x)/((pi/4-x)(cos ...

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  20. Evaluate the following limit: lim(x->pi/4)(1-t a n x)/(1-sqrt(2)sin x)

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