How do you find #lim (x+5)(1/(2x)+1/(x+2))# as #x->oo# using l'Hospital's Rule or otherwise?

1 Answer
Jim H
Dec 27, 2016

I would do some algebra first

Explanation:

# (x+5)(1/(2x)+1/(x+2)) = (x+5)(((x+2)+(2x))/(2x(x+2)))#

# = ((x+5)(3x+2))/(2x(x+2))#

# = (3x^2+17x+10)/(2x^2+4x)#

Quick result

Because the degrees of the top and bottom are the same, the limit at infinity is the ratio of the leading coefficients:

#lim_(xrarroo)(x+5)(1/(2x)+1/(x+2)) = lim_(xrarroo)(3x^2+17x+10)/(2x^2+4x)#

# = 3/2#

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