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Evaluate lim 1/x - log(1 +x)/x2

  • Evaluate lim   〈   1 - log(1 + x)〉
                  x→0         x         x2

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Michael F. | Mathematics TutorMathematics Tutor
4.6 4.6 (5 lesson ratings) (5)
1
For small values of x     ln(1+x)~x-x2/2+x3/3-...
1/x-(ln(1+x))/x2=1/x-(x-x2/2+x3/3-...)/x2=1/x-1/x+1/2+x/3-...which =1/2 as x→0
Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
5.0 5.0 (3 lesson ratings) (3)
0
Use l'Hospital's Rule twice:
 
limx→0 1/x - ln(1+x)/x²
= lim (x - ln(1+x))/x²
= lim (1- 1/(x+1) )/2x
= lim (x/(2x+2x²))
= lim (1/(2+4x))
= 1/2