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How do you evaluate #(x−4 )/ (x^2+6x−40)# as x approaches 4?

Answer 1

Paisley Johnson

#lim_(xrarr4)(x-4)/(x^2+6x-40)=1/14#

Given,

#lim_(xrarr4)(x-4)/(x^2+6x-40)#

Factor the denominator.

#=lim_(xrarr4)(x-4)/((x+10)(x-4))#

Cancel the factors, #x-4# in the numerator and denominator.

#=lim_(xrarr4)color(red)cancelcolor(black)(x-4)/((x+10)color(red)cancelcolor(black)((x-4)))#

#=lim_(xrarr4)1/(x+10)#

Substitute #x=4#.

#=lim_(xrarr4)1/((4)+10)#

#=lim_(xrarr4)1/14#

#=1/14#

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Answer 2

William Abdalla

To evaluate (x−4)/(x^2+6x−40) as x approaches 4, substitute 4 for x in the expression.

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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.