it should be x + 3 and not x - 3. x - 3 is negative and there is no logarithm possible for that.

sir its written x-3 it could be wrong ...

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it should be x + 3 and not x - 3. x - 3 is negative and there is no logarithm possible for that.

sir its written x-3 it could be wrong ...

Log in to add a comment

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1) This question does not seem to be correctly written. please check. Is it x+3 in the numerator ?

Lim [ Log (x+3) ] / (x+2)

x -> -2

We use the Taylor series expansion for Log (1+h) = h - h²/2 + h³/3 - h⁴/4 + ...

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2)

Let x/e -1 = h . Hence, as x -> e, h -> 0.

We use the Taylor's series for expansion of Log (1 + h) as in the above problem.

The limit is

Lim [ Log (x+3) ] / (x+2)

x -> -2

We use the Taylor series expansion for Log (1+h) = h - h²/2 + h³/3 - h⁴/4 + ...

=======================

2)

Let x/e -1 = h . Hence, as x -> e, h -> 0.

We use the Taylor's series for expansion of Log (1 + h) as in the above problem.

The limit is