How do you find the limit of #(x^2 + 3) / (x - 2)# as x approaches 2-?

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Answer 1 · 2016-04-28T01:41:28

#lim_(xrarr2^-)(x^2+3)/(x-2)=-infty#

Given,

#lim_(xrarr2^-)(x^2+3)/(x-2)#

Break apart the fraction.

#=lim_(xrarr2^-)(x^2+3)(1/(x-2))#

Recall that "the limit of a product is the product of the limits, provided the limits exist."

#=lim_(xrarr2^-)x^2+3*lim_(xrarr2^-)1/(x-2)#

Substitute #x=2^-#.

#=lim_(xrarr2^-)(2^-)^2+3*lim_(xrarr2^-)1/((2^-)-2)#

#=lim_(xrarr2^-)4+3*lim_(xrarr2^-)1/0^-#

#=lim_(xrarr2^-)7*-infty#

Recall that "the limit of a constant is equal to the constant."

#=7*-infty#

#=-infty#