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Evaluate the following limit: (lim)(thet...

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

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`(lim)_(theta->0)(sin4theta)/(ta n 3theta)`

We know,

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

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

`(lim)_(theta->0)(4 theta (sin4theta)/(4 theta))/(3 theta (ta n 3theta)/(3theta))`

`(lim)_(theta->0)(4 theta)/(3 theta)=4/3`

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

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

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

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

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

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

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

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

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

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