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

Answer 1

Charles Anctil

# 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#.

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Answer 2

Paisley Johnson

#12#

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

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

The sum of two cubes is the factor numerator.

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

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

Factors that cancel:

#(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#

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Answer 3

Paisley Johnson

The limit of ( \frac{x^3 + 8}{x + 2} ) as ( x ) approaches ( -2 ) is ( 0 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.