What is wrong with the application of L'Hopital's rule to <munder> <mo movablelimits="true" f

Laurel Yoder

Laurel Yoder

Answered question

2022-05-22

What is wrong with the application of L'Hopital's rule to lim x 2 x 2 7 x + 10 x 2 + x 6

Answer & Explanation

Philip Deleon

Philip Deleon

Beginner2022-05-23Added 4 answers

It holds x 2 7 x + 10 = ( x 2 ) ( x 5 ) and x 2 + x 6 = ( x 2 ) ( x + 3 ) . Hence, we have
x 2 7 x + 10 x 2 + x 6 = ( x 5 ) ( x 2 ) ( x + 3 ) ( x 2 ) = x 5 x + 3
for all x { 3 , 2 }. Hence, the pole x = 2, such that the function is still continuous. So your result 3 5 is correct, because 2 5 2 + 3 = 3 5

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