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

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

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`(lim)_(x->0)(sin ax+bx)/(a x+sin bx)`

L'Hopital Rule:

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

`(lim)_(x->0)(sin ax+bx)/(a x+sin bx)=(lim)_(x->0)(acosax+b)/(a+bcos bx)`

`(lim)_(x->0)(acosax+b)/(a+bcos bx)=(acos0+b)/(a+bcos0)`

`=(a+b)/(a+b)=1`

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RD SHARMA-LIMITS-All Questions
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  2. Evaluate the following limit: (lim)(x->0)(3sin x-sin3x)/(x^3)

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Evaluate the following limit: (lim)(x->pi/4)(f(x)-f(pi/4))/(x-pi/4) , ...

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  17. Evaluate the following limit: lim(x->1)(1-x^2)/(sinpix)

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

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  19. Evaluate the following limit: (lim)(n->oo)2^(n-1)sin(a/(2^n))

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

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