How to find limit of (3e^x - e^-x -2)/x if x approaches 0?

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Answer 1 · 2017-11-28T14:07:34

# 4#.

We will use the #"Standard Limit : "lim_(x to 0)(e^x-1)/x=lne=1.#

Now, #"The Reqd. Limit="lim_(x to 0)(3e^x-e^-x-2)/x,#

#=lim (3e^x-1/e^x-2)/x,#

#=lim (3e^(2x)-2e^x-1)/(xe^x),#

#=lim {(e^x-1)(3e^x+1)}/(xe^x),#

#=lim_(x to 0){(e^x-1)/x}{(3e^x+1)/e^x},#

#={1}{(3e^0+1)/e^0},#

#=4.#