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## Homework Statement

question attached.

My question is just about the size of the limit, how do you know whether to expand out the exponential or not (parts 2) and 4))

## Homework Equations

for small ##x## we can expand out ##e^{x} ## via taylor series.

## The Attempt at a Solution

Solutions given here for parts 2) and 4) respectively. (not full sol but only as relevant as needed for the question):

For parts 2) and 4) below I would have used the same approximation ##1+3e^{x}##, but would have expanded out the exponential as ##1+x##.

I'm just wondering how you know whether or not to expand this out or not, going by 'low ##T## many thanks.