What is the limit as x approaches -2 from the right of the following equation?

Question

limit of f(x) as x approaches -2 from the right of #(x+2)/(2x^2+5x+2)#

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Answer 1 · 2018-02-06T06:09:02

# -1/3#.

Note that, #(x+2)/(2x^2+5x+2)=(x+2)/{(x+2)(2x+1)}#.

#:. (x+2)/(2x^2+5x+2)=1/(2x+1), if xne-2#.

Now, as # x to -2+, x gt -2," hence, "x ne -2#.

#:. lim_(x to -2+)(x+2)/(2x^2+5x+2)#,

#=lim_(x to -2+)1/(2x+1)#,

#=1/{2(-2)+1}#.

# rArr lim_(x to -2+)(x+2)/(2x^2+5x+2)=-1/3#.