Baixe o app para aproveitar ainda mais
Prévia do material em texto
Exercícios - Pré cálculo Limites 01 Determine os limites: a) 𝑥 3 lim → 𝑥²−9 𝑥−3 = 𝑥 3 lim → 𝑥²−9 𝑥−3 𝑥 3 lim → 𝑥+3( ) 𝑥−3( ) 𝑥−3 = 𝑥 3 lim → 𝑥 + 3 = 3 + 3 = 6 b) 𝑥 5 lim → 5−𝑥 25−𝑥² 𝑥 5 lim → 5−𝑥 25−𝑥² = 𝑥 5 lim → 5−𝑥 5+𝑥( ) 5−𝑥( ) = 𝑥 5 lim → 1 5+𝑥 = 1 5+5 = 1 10 c) 𝑥 0 lim → 𝑥³ 2𝑥²−𝑥 𝑥 0 lim → 𝑥³ 2𝑥²−𝑥 = 𝑥 0 lim → 𝑥³ 2𝑥−1( )𝑥 = 𝑥 0 lim → 𝑥² 2𝑥−1 = 0² 2*0−1 = 0 1 = 0 d) 𝑥 2 lim → 𝑥³−8 𝑥−2 𝑥 2 lim → 𝑥³−8 𝑥−2 = 𝑥 2 lim → 𝑥³−8 𝑥−2 = 𝑥 2 lim → 𝑥²+2𝑥+4( ) 𝑥−2( ) =𝑥−2 = 𝑥 2 lim → 𝑥² + 2𝑥 + 4( ) 𝑥 2 lim → 𝑥³−8 𝑥−2 = 𝑥 2 lim → 𝑥² + 2𝑥 + 4( ) = 2² + 2 * 2 + 4( ) = 4 + 4 + 4 = 12 e) 𝑥 1 lim → 𝑥²−4𝑋+3 𝑥³−1 𝑥 1 lim → 𝑥²−4𝑋+3 𝑥³−1 = 𝑥 1 lim → 𝑥−1( ) 𝑥−3( ) 𝑥−1( ) 𝑥²+𝑥+1( ) = 𝑥 1 lim → 𝑥−3 𝑥²+𝑥+1 = 1−3 1²+1+1 =− 2 3 f) 𝑥 0 lim → 1−2𝑥−𝑥²−1 𝑥 𝑥 0 lim → 1−2𝑥−𝑥²−1 𝑥 = 𝑥 0 lim → 1−𝑥( )²−1 𝑥 = 𝑥 0 lim → 1−𝑥( )−1 𝑥 = 𝑥 0 lim → −𝑥 𝑥 = 𝑥 0 lim → − 1 =− 1 g) 𝑥 0 lim → 1+𝑥− 1−𝑥 𝑥 1+𝑥− 1−𝑥 𝑥 = 1+𝑥− 1−𝑥 𝑥 × 1+𝑥+ 1−𝑥 1+𝑥+ 1−𝑥 = 1+𝑥( )− 1−𝑥( ) 𝑥* 1+𝑥+ 1−𝑥( ) = 1+𝑥−1+𝑥 𝑥* 1+𝑥+ 1−𝑥( ) = = 2𝑥 𝑥* 1+𝑥+ 1−𝑥( ) = 2 1+𝑥+ 1−𝑥( ) ⇒ 𝑥 0 lim → 1−2𝑥−𝑥²−1 𝑥 = 𝑥 0 lim → 2 1+𝑥+ 1−𝑥( ) = 2 1+0+ 1−0( ) = 2 1+ 1 = 22 = 1 h) 𝑥 1 lim → 2𝑥− 𝑥+1 𝑥−1 2𝑥− 𝑥+1 𝑥−1 = 2𝑥− 𝑥+1 𝑥−1 × 2𝑥+ 𝑥+1 2𝑥+ 𝑥+1 = 2𝑥− 𝑥+1( ) 𝑥−1( ) 2𝑥+ 𝑥+1( ) = 𝑥−1 𝑥−1( ) 2𝑥+ 𝑥+1( ) = 1 2𝑥+ 𝑥+1( ) 2𝑥− 𝑥+1 𝑥−1 = 𝑥 1 lim → 1 2𝑥+ 𝑥+1( ) = 1 2*1+ 1+1( ) = 1 2+ 2( ) = 1 2 2 = 24
Compartilhar