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Member warned about not using the homework template

Hi,

I'm trying to find the limit as x tends to zero of the function (tanhx-x)/x

this is what i have but i have no idea if i am on the right lines?

lim x-> 0 can be split up into two problems:

limx->0 (tanhx)/x - limx->0 x/x

limx->0 x/x = 1

limx->0 (tanhx)/x can be expressed as

limx->0 ((e^x-e^-x)/e^x+e^-x))/x

=

limx->0 (x(e^x-e^-x)/e^x+e^-x)) =0

which leave the limit as -1 but wolfram gives a limit of 0

how should i be approaching this problem?

many thanks

Ryan

I'm trying to find the limit as x tends to zero of the function (tanhx-x)/x

this is what i have but i have no idea if i am on the right lines?

lim x-> 0 can be split up into two problems:

limx->0 (tanhx)/x - limx->0 x/x

limx->0 x/x = 1

limx->0 (tanhx)/x can be expressed as

limx->0 ((e^x-e^-x)/e^x+e^-x))/x

=

limx->0 (x(e^x-e^-x)/e^x+e^-x)) =0

which leave the limit as -1 but wolfram gives a limit of 0

how should i be approaching this problem?

many thanks

Ryan