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Evaluate the following limit: (lim)(x->0...

Evaluate the following limit: `(lim)_(x->0)(x\ cos x-sin x)/(x^2+t a n x)`

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Verified by Experts

`(lim)_(x->0)(x\ cos x-sin x)/(x^2+t a n x)`

We know,

`(lim)_(x->0) (sin x)/(x)=1`

`(lim)_(x->0) (tan x)/(x)=1`

`(lim)_(x->0) (x\ cos x-x)/(x^2+x)`

`(lim)_(x->0) (cos x-1)/(x+1)`

L'Hopital Rule:

`lim_(x rightarrow b) (f(x))/(g(x))=lim_(x rightarrow b) (f'(x))/(g'(x))`

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RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: lim(x->0)(5x+4sin3x)/(4sin2x+7x)

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  2. Evaluate the following limit: lim(x->0)(cos e c x-cot x)

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  3. Evaluate the following limit: (lim)(x->0)(x\ cos x-sin x)/(x^2+t a n x...

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  4. Evaluate the following limit: (lim)(theta->0)(1-cos4theta)/(1-cos6thet...

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  5. Evaluate the following limit: (lim)(theta->0)(sin4theta)/(ta n 3theta)

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  6. Evaluate the following limit: (lim)(x->0)(1-cos5x)/(1-cos6x)

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  7. Evaluate the following limit: (lim)(x->0)(sin3x+7x)/(4x+sin2x)

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  8. Evaluate the following limit: (lim)(x->0)(3sin x-sin3x)/(x^3)

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  9. Evaluate the following limit: (lim)(x->0)(sin ax+bx)/(a x+sin bx)

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  10. Evaluate: lim(h->0)((a+h)^2sin(a+h)-a^2sina)/h

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  11. If (lim)(x->0)k x\ cosec\ x=(lim)(x->0) xcosec\ k x , find k

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  12. Evaluate: (lim)(x->pi/2)(cot x)/(pi/2-x)

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  13. Evaluate: (lim)(x->pi/2)(pi/2-x)t a n x

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  14. (lim)(x->pi/2)(tan2x)/(x-pi/2)

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  15. Evaluate the following limits: lim(x->pi/2)(pi/2-x)tanx

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  16. Evaluate the following limit: lim(x->pi/2)(cos^2x)/(1-sin x)

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

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  18. Evaluate the following limit: (lim)(x->pi/2)(1-sin x)/((pi/2-x)^2)

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  19. Evaluate the following limit: (lim)(x->pi/8)(cot4x-cos4x)/((pi-8x)^3)

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  20. Evaluate the following limit: (lim)(x->pi)(sqrt(5+cos x)-2)/((pi-x)^2)

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