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

Evaluate the following:`lim_(xtoinfty) sinx/x`

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`0lt|sinx/x|le1/|x|`
`implies0lelim_(xtoinfty)|sinx/x|lelim_(xtoinfty)1/|x|`
`0lelim_(xtoinfty)|sinx/x|le0`
`implieslim_(xtoinfty)(sinx/x)=0`
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MBD PUBLICATION-LIMIT AND DIFFERENTIATION-QUESTION BANK
  1. lim(xto1)f(x) if f(x)={(2x-1, xle1), (2x+1, xgt):}

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  2. lim(xto0)f(x)and lim(xto1)f(x) if f(x)={(0cdot xle0, xle1), (1-2x, 0...

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  3. Evaluate the following:lim(xtoinfty) sinx/x

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  4. Evaluate the following:lim(xtoinfty)x(a^(1/x)-1), agt0

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  5. Evaluate the following:lim(xto0)(x^(1/2)+2x+3x^(3/2))/(2x^(1/2)-2x^(5/...

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  6. Evaluate the following:lim(xtoinfty)sqrtx{sqrt(x+1)-sqrtx}

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  7. Evaluate the following:lim(xtoinfty)x^2{sqrt(x^4+a^2)-sqrt(x^4-a^2)}

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  8. Evaluate the following:lim(xto0) cos(sin x)

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  9. Evaluate the following:lim(xto0) (sqrt(1+x)-1)/loge(1-x)

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

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

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

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

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

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

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

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

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

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

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

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