limit x-> 1 x²-1/x-1 + x²+3x+2/x²-4x+3 mohon dengan penjelasannya
Matematika
berliandifiaaaa
Pertanyaan
limit x-> 1
x²-1/x-1 + x²+3x+2/x²-4x+3
mohon dengan penjelasannya
x²-1/x-1 + x²+3x+2/x²-4x+3
mohon dengan penjelasannya
1 Jawaban
-
1. Jawaban andhikahanif
penyelesaian
Limit x --> 1
( (x² - 1) / (x - 1) ) + ( (x² + 3x + 2) / (x² - 4x + 3) )
= Limit x --> 1
( ( (x - 1) (x + 1) ) / (x -1) ) + ( (x² + 3x + 2) / ( (x - 3) (x - 1) ) )
= Limit x --> 1
( (x + 1) / (x - 1) ) + ( (x² + 3x + 2) / ( (x - 3) (x - 1) ) )
= Limit x --> 1
( (x + 1) (x - 3) / (x - 1) (x - 3) ) + ( (x² + 3x + 2) / ( (x - 3) (x - 1) ) )
= Limit x --> 1
( (x² - 2x -3) / (x - 3) (x - 1) ) + ( (x² + 3x + 2) / ( (x - 3) (x - 1) ) )
= Limit x --> 1
(x² - 2x -3) + (x² + 3x + 2) / ( (x - 3) (x - 1) )
= Limit x --> 1
(2x² +x -1) / (x² - 4x + 3)
= (2(1)² +(1) -1) / ( (1)² - 4(1) + 3)
= 2 / 0
= ∞