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Evaluate the following limits: lim(xrar...

Evaluate the following limits: `lim_(xrarra)((sinx-sina))/((sqrtx-sqrta))`

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Verified by Experts

The correct Answer is:
`2sqrtacosa`
Given limit `=lim_(xtoa)(2cos((x+a)/(2))sin((x-a)/(2)))/((x-q))xx(sqrtx+sqrta)`
`=lim_(xtoa){cos((x+a)/(2)).(sin((x-a)/(2)))/(((x-a)/(2)))xx(sqrtx+asqrta)}`
`(cosaxx1xx2sqrta)=2sqrtacosa.`
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RS AGGARWAL-LIMIT-EXERCISE 27B
  1. Evaluate the following limits: lim(xrarra)((sinx-sina))/((x-a))

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  2. Evaluate the following limits: lim(xrarra)((sinx-sina))/((x-a))

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  3. Evaluate the following limits: lim(xrarra)((sinx-sina))/((sqrtx-sqrta...

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  4. Evaluate the following limits: lim(xrarr0)((sin5x-sin3x))/(sinx)

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  5. Evaluate the following limits: lim(xrarr0)((cos3x-cos5x))/(x^(2))

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  6. Evaluate the following limits: lim(xrarr0)((sin3x+sin5x))/((sin6x-si...

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  7. Evaluate the following limits: lim(xrarr0)([sin(2+x)-sin(2-x)])/(x)

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  8. Evaluate the following limits: lim(xrarr0)((1-cos2x))/((cos2x-cos8x)...

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

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  10. Evaluate the following limits: lim(xrarr0)((sqrt(1+2x)-sqrt(1-2x)))/...

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  11. Evaluate the following limits: lim(xrarr0)((e^(tan-x)-1))/(tanx)

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  12. Evaluate the following limits: lim(xrarr0)((e^(3+x)-sinx-e^(3)))/(x)

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  13. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(tanx)

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  14. Evaluate the following limits: lim(xrarr0)((e^(tanx)-1))/(x)

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  15. Evaluate the following limits: lim(xrarr0)(ax+x cosx)/(b sinx)

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  16. Evaluate the following limits: lim(xrarr0)(sinax+bx)/(ax+sinbx),wher...

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  17. lim(x->pi)(sin(pi-x)/(pi(pi-x)))

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  18. lim(x->pi/2) (tan 2x)/(x-pi/2)

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  19. Evaluate the following limits: lim(xrarr0)(cos2x-1)/(cosx-1)

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  20. Evaluate the following limits: lim(xrarr0)(cosec x-cotx)

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