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Examine the existence of the following l...

Examine the existence of the following limits:`lim_(xto0)` cosecx

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L.H.L.`=lim_(xto0-)` cosecx
`=lim_(hto0)` cosec(-h)
`=lim_(hto0)` -1/sin h`=-infty`
R.H.L.`=lim_(hto0+)`cosecx
`=lim_(hto0)`cosec(h)=`infty`
As L.H.L.neR.H.L. the limit does not exist.
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MBD PUBLICATION-LIMIT AND DIFFERENTIATION-QUESTION BANK
  1. Examine the existence of the following limits:lim(xto0+) logax

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  2. Examine the existence of the following limits:lim(xto pi/2) tanx

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  3. Examine the existence of the following limits:lim(xto0) cosecx

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  4. Examine the existence of the following limits:lim(xto0-)e^(1/x)

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  5. Examine the existence of the following limits:lim(xto0+)e^(1/x)

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  6. Examine the existence of the following limits:lim(xto0)1/(e^(1/x)-1)

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  7. Find the value of a if, lim(xtoalpha)(tana(x-alpha))/(x-alpha)=1/2

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  8. Find the value of a if,lim(xto0)(tanax)/(sin2x)=1

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  9. Find the value of a if,lim(xto0)(e^(ax)-e^x)/x=2

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  10. Find the value of a if,lim(xto1)(5^x-5)/((x-1)logea)=5

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  11. Find the value of a if,lim(xto2)loge(2x-3)/(a(x-2))=1

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  12. Find the derivative of the following functions 'ab initio', that is, u...

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  13. Find the derivative of the following functions 'ab initio', that is, u...

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  14. Find the derivative of the following functions 'ab initio', that is, u...

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  15. Find the derivative of the following functions 'ab initio', that is, u...

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  16. Find the derivative of the following functions 'ab initio', that is, u...

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  17. Find the derivative of the following functions 'ab initio', that is, u...

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  18. Find the derivative of the following functions 'ab initio', that is, u...

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  19. Find the derivative of the following functions 'ab initio', that is, u...

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  20. Find the derivative of the following functions 'ab initio', that is, u...

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