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Evaluate the following:lim(xtoinfty)loge...

Evaluate the following:`lim_(xtoinfty)log_e``(1+a/x)^x`

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`lim_(xtoinfty)log_e``(1+a/x)^x`
`=log_e{lim_(xtoinfty)(1+a/x)^x}`
`log_ee^a=alog_e`
`e=a[thereforelim_(x to infty)(1+a/x)^x=e^a
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MBD PUBLICATION-LIMIT AND DIFFERENTIATION-QUESTION BANK
  1. Evaluate the following:lim(xto0) (sqrt(1+x)-1)/loge(1-x)

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  2. Evaluate the following:lim(xto2)log2(x^2-4)/(sqrt(3x-2)-sqrt(x+2)

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  3. Evaluate the following:lim(xtoinfty)loge(1+a/x)^x

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  4. Evaluate the following:lim(xto0)loge(1+bx)^(1/x)

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  5. Evaluate the following:lim(xto pi/4) sin((1-tanx)/(1+tanx))/(pi/4-x)

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  6. Evaluate the following:lim(xto pi/2)log (1-sin^3x)/cos^2x

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  7. Evaluate the following:lim(xtoinfty)e^x(a^(1/x)-1)

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  8. Evaluate the following:lim(xto0)(x(e^(sqrt(1+x^2+x^4-1)/x-1)))/(sqrt(1...

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  9. Examine the existence of the following limits:lim(xto0+) logax

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

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

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

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

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

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

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

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

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

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

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

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