Evaluate #lim_(xto0)(e^x-e^(-x))/(e^x+e^(-x))#?
1 Answer
Mar 8, 2018
# lim_(x -> 0)(e^x-e^(-x))/(e^x+e^(-x)) = 0#
Explanation:
Method 1:
Direct Substitution gives us:
# lim_(x -> 0)(e^x-e^(-x))/(e^x+e^(-x)) = (1-1)/(1+1) = 0#
Method 1:
Using hyperbolic functions:
# lim_(x -> 0)(e^x-e^(-x))/(e^x+e^(-x)) = lim_(x -> 0)((e^x-e^(-x))/2)/((e^x+e^(-x))/2) #
# " " = lim_(x -> 0) (sinhx/coshx) #
# " " = lim_(x -> 0) (tanhx) #
# " " = tanh0 #
# " " = 0 #
