Can anyone find the value and if possible show every step? Thanks in advance.

Question

#Lim_(xrarr-oo) (1/e^x-1/((3pi)/2-tanhx))#

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Answer 1 · 2017-12-04T14:14:13

Please see below.

#lim_(xrarr-oo)1/e^x = lim_(xrarroo)e^x = oo#

#lim_(xrarr-oo)tanh(x) = -1# so

#lim_(xrarr-oo)1/((3pi)/2-tanhx) = 1/((3pi)/2+1)# and

#lim_(xrarr-oo)(1/e^x-1/((3pi)/2-tanhx) ) = oo - 1/((3pi)/2+1) = oo#