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Find the following limits:lim(xrarr0+)(e...

Find the following limits:`lim_(xrarr0+)(e^(-1/x))/(x)`

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`lim_(xrarr0+)(e^(-1/x))/(x)` (0/0 form)
`[Put 1/x=y`
As `xrarr0, ytoinfty`
`=lim_(yrarrinfty)(e^-y/1)/(1/e^y)=lim_(yrarrinfty)y/e^y(infty/infty` form)
`lim_(yrarrinfty)1/e^y=0`
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MBD PUBLICATION-APPLICATION OF DERIVATIVES-QUESTION BANK
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  2. Find the following limits:lim(xrarrinfty)(In(1/x))/(xe^x)

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  3. Find the following limits:lim(xrarr0+)(e^(-1/x))/(x)

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  4. Find the following limits:lim(xrarrinfty)(x^n+x^(-n))/(x+2)^n

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  5. Find the following limits:lim(xrarr0)(e^x-e^(-x))/(xcosx)

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  6. Find the following limits:lim(xrarrinfty)(sin^(-1)x)/(x)

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  7. Find the following limits:lim(xrarr0+)logtanx tan2x

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  8. Find the following limits:lim(xrarrpi/2)(tanx)^cosx

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  9. Find the following limits:lim(xrarr1)x^(1/(1-x)

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  10. Find the following limits:lim(xrarr0+)x^(sinx)

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  11. Find the following limits:lim(xrarr1)(1/(x-1)-1/(lnx))

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  12. Find the following limits:lim(xrarrinfty)(x-sqrt(x^2-1))

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  13. Find the following limits:lim(xrarrinfty)(x-sqrt(x^2+2x))

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  14. Find the following limits:lim(xrarr0)(1/sin^2x-1/x^2)

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  15. Find the following limits:lim(xrarrpi/2)(tan3x-tanx)

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  16. Find the following limits:lim(xrarr0+)sqrt(a^x-b^x)/sqrtx, agtb

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  17. Find the following limits:lim(xrarrinfty)(1+3/x)^x

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  18. Find the following limits:lim(xrarrinfty)(e^(1/x))^(ln(1+x))

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  19. Find the following limits:lim(xrarr0)(sinx/x)^(1/x)

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  20. Find the following limits:lim(xrarr0)(1+x^2)^(1/x)

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