Find the limit. lim_(u rightarrow 1) (u^4 -1)/(u^3 -1)

Marco Hudson

Marco Hudson

Answered question

2022-08-07

Find the limit.
lim u 1 ( u 4 1 ) / ( u 3 1 )

Answer & Explanation

Kelsie Marks

Kelsie Marks

Beginner2022-08-08Added 17 answers

lim u 1 u 4 1 u 3 1
factor both the numerator and denominator.
numerator: ( u 2 1 ) ( u 2 + 1 ) = ( u 1 ) ( u + 1 ) ( u 2 + 1 )
denominator: ( u 1 ) ( u 2 + u + 1 )
since the (u - 1) cancels we are left with.
lim u 1 u 4 1 u 3 1 = lim u 1 ( u + 1 ) ( u 2 + 1 ) u 2 + u + 1 = 4 3

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