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

Evaluate: `(lim_(n->oo)ncos(pi/(4n))sin(pi/(4n))`

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`lim_(n->oo)ncos(pi/(4n))sin(pi/(4n))`
Take `1/n=t`
Then
`lim_(t->0)1/t cos((tn)/4)sin((tn)/4)`
`lim_(t->0)(pi/4 cos((tn)/4)sin((tn)/4))/((tn)/4)`
`lim_(t->0) pi/4 cos((tn)/4) xx lim_(t->0) sin((t pi)/4)/((t pi)/4)`
`=lim_(t->0) pi/4 cos((tn)/4) xx 1`
`=pi/4 cos(0)`
...
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RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: lim(x->1)(1+cospix)/((1-x)^2)

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

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

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

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

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

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

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

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

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

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

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

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  13. Evaluate the following limit: lim(x->pi)(1+cos x)/(tan^2x)

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  14. Evaluate the following limit: lim(x->pi/6)(cot^2x-3)/(cos e c x-2)

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  15. Evaluate the following limit: lim(x->pi/4)(2-cos e c^2x)/(1-cot x)

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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->(3pi)/2)(1+cos e c^3x)/(cot^2x)

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  18. Evaluate: lim(x->e)(logx-1)/(x-e)

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  19. Evaluate the following limit: lim(x->0)(5^x-1)/(sqrt(4+x)-2)

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  20. Evaluate the following limit: lim(x->0)(a^x+b^x-2)/(x^(2\ ))

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