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

Evaluate the following limit: `(lim)_(x->0)(sin(3+x)-sin(3-x))/x`

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`(lim)_(x->0)(sin(3+x)-sin(3-x))/x`

L'Hopital Rule:

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

`(lim)_(x->0)(cos(3+x)+cos(3-x))/1`

`=(cos(3+0)+cos(3-0))/1`

`=2cos(3^o)`

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RD SHARMA-LIMITS-All Questions
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  2. Evaluate the following limit: (lim)(x->0)(x^3cotx)/(1-cos x)

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

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  4. lim(x->0)(tan8x)/(sin2x)

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  5. lim(x->0)(sin5x)/(tan3x)

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  6. lim(x->0)(7xcosx-3sinx)/(4x+tanx)

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  7. Evaluate the following limit: (lim)(x->0)(tan^2 3x)/(x^2)

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  8. Evaluate the following limit: (lim)(x->0)(3sin2x+2x)/(3x+2tan3x)

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  9. Evaluate the following limit: (lim)(theta->0)(sin3theta)/(tan2theta)

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  10. Evaluate the following limit: lim(x->0)(sin^2 4x^2)/(x^4)

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  11. Evaluate the following limit: lim(x->0)(2x-sin x)/(tanx+x)

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  12. Evaluate the following limit: lim(x->0)(sin3x-sin x)/(sinx)

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  13. Evaluate the following limit: lim(x->0)(cos3x-cos5x)/(x^2)

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  14. Evaluate the following limit: lim(x->0)(sin(2+"x")-"sin"(2-"x"))/"x"

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  15. Evaluate the following limit: lim(x->0)(t a n x-sin x)/(sin3x-x sin x)

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  16. Evaluate the following limit: lim(x->0)(1-cos2x)/(cos2x-cos8x)

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  17. Evaluate the following limit: lim(x->oo) (sin(a+x) + sin(a-x) - 2 sin ...

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  18. Evaluate the following limit: lim(x->0)(x^2+1-cos x)/(xsinx)

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  19. Evaluate the following limit: lim(x->0)(2sin x^0-sin2x^0)/(x^3)

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  20. Evaluate the following limit: lim(x->0)(xtanx)/(1-cos2x)

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