The value of Lim x->1 (x^5-3x+2)/x-1 is equal to?

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Answer 1 · 2018-02-09T08:03:34

#lim_(x->1) (x^5-3x+2)/(x-1) =2#

#lim_(x->1) (x^5-3x+2)/(x-1) #

Applying synthetic division:

# (x^5-3x+2)/(x-1) = (x^4+x^3+x^2+x-2)#

Hence, #lim_(x->1) (x^5-3x+2)/(x-1) = lim_(x->1) (x^4+x^3+x^2+x-2)#

#= 1+1+1+1-2 =2#

NB: We can verify this result by application of L'Hopital's rule, as follows:

#lim_(x->1) (x^5-3x+2)/(x-1)# is of the inderminant form #0/0#

#= lim_(x->1)(d/dx(x^5-3x+2))/ (d/dx(x-1)#

#= lim_(x->1) (5x^4-3)/1#

#= (5-3)/1= 2#