Lim (X^3+8/x+2). ? X=-2

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Answer 1 · 2018-01-11T11:56:32

# 12#.

#"The Reqd. Lim.="lim_(x to -2)(x^3+8)/(x+2)#,

#=lim{(x+2)(x^2-2x+4)}/(x+2)#,

#=lim_( x to-2)(x^2-2x+4)#,

#=(-2)^2-2(-2)+4#,

#=12#.

Answer 2 · 2018-01-11T12:03:22

#12#

#lim_(x->-2)((x^3+8)/(x+2))#

#(x^3+8)/(x+2)=>(x^3+2^3)/(x+2)#

Factor numerator: ( Sum of two cubes )

#(a^3+b^3)=(a+b)(a^2-ab+b^2)#

#((x+2)(x^2-2x+4))/(x+2)#

Cancel factors:

#(cancel((x+2))(x^2-2x+4))/cancel((x+2))#

#x^2-2x+4#

Plug in #-2#

#(-2)^2-2(-2)+4=12#

#:.#

#lim_(x->-2)((x^3+8)/(x+2))=12#