Question #1feda

1 Answer
Jim H
Mar 12, 2017

#e^4#

Explanation:

#lim_(x -> oo) ((x+3)/(x-1))^(x+3)#

I shall use #lim_(hrarroo)(1+1/h)^h = e#.

Let #t=x-1#, so that #x+3 = t+4# and we need to find

#lim_(trarroo) ((t+4)/t)^(t+4) = lim_(trarroo) (1+4/t)^t * lim_(trarroo) (1+4/t)^4 #

# = lim_(trarroo) ((1+1/(t/4))^(t/4))^4 * 1^4#

# = lim_(trarroo) ((1+1/(t/4))^(t/4))^4#

# = (lim_(trarroo) (1+1/(t/4))^(t/4))^4#

# = e^4#

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