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

Evaluate the following limit: `(lim)_(x->a)(cos x-cos a)/(x-a)`

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`lim_(x->a)(cos x-cos a)/(x-a)`

L'Hopital Rule:

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

`lim_(x->a)(cos x-cos a)/(x-a)`

Applying L'Hopital Rule:

`lim_(x->a) (-sin x-0)/(1-0)=lim_(x->a) (-sinx)`

`=-sin a`

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

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

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

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

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

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

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

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

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

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

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

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  13. Evaluate lim(x->pi/3)(sqrt(1-cos6x))/(sqrt2(pi/3-x))

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  14. Evaluate the following limit: lim(x->pi/4)(1-t a n x)/(x-pi/4)

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  15. Evaluate the following limit: lim(x->pi/3)(sqrt(3)-t a n x)/(pi-3x)

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

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

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

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  19. Evaluate the following limit: lim(x->a)(cossqrt(x)-cossqrt(a))/(x-a)

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  20. Evaluate the following limit: lim(x->1)(1+cospix)/((1-x)^2)

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