GABARITO EVA FINAL ( M2 )

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GABARITO EVA FINAL – 2021.1 
TURMA M2 
QUESTÃO 01 
 Sejam f e g funções tais que, f(1) = 2 , g(1) = 1, f’(1) = 3 e g’(1) = 4. Calcule : 
 a) sendo H(x) = f(x).g(x) , então H’(x) = f(x)’.g(x) + f(x).g’(x) ( DERIVADA DO PRODUTO ) 
 H’(1) = f(1)’.g(1) + f(1).g’(1) 
 H’(1) = 3.1 + 2.4 ( 1,0 PONTO ) 
 
 b) g(1) = 1, g’(1) =1 e f’(1) = 3, ache f(1) . 
 ( ) ( ) √ 
 ( ( ) ( )) ( √ ) 
 ( ) ( ) ( ) ( ) 
 
 √ 
 
 ( ) ( ) ( ) ( ) 
 
 √ 
 
 ( ) ( 1,0 PONTO ) 
 
QUESTÃO 02 
 a) ( ) 
 
√ 
 
 
 ( 1,0 PONTO ) 
 
 b) ( ) 
 ( 1,0 PONTO ) 
 
QUESTÃO 03 
 a) Tg 
 
 
 ( 1,0 PONTO ) 
 
 
 
H’(1) = 11 
 𝑦 ( 𝑒𝑥 𝑠𝑒𝑛 𝑥 ) ( 𝑒𝑥 𝑥 ) 
 
𝑦 
− ( 𝑥 𝑥 𝑦 )
𝑥 𝑦 𝑦 
 
f(1) = 2 
𝑓´(𝑥) 
 𝑥2 𝑥 √𝑥 𝑥 − ( 𝑥 𝑥 )( 
1
2√𝑥
 
1
𝑥
 )
( √𝑥 𝑥 ) 
 
 b) ( )√ 
 √ ( ) 
 
 
 
 
 
 √ 
 ( ) √ 
 
 
 
 
 ( 1,0 PONTO ) 
 
 QUESTÃO 04 
 ( ) − ( ) ( ) 
 
 ( ) − − 
 
 
 
 ( ) 
 
 
 −
 
 
 
 
 
 −
 
 
 − 
 
 
 ( 2,0 PONTOS ) 
QUESTÃO 05 
a) ∫ √ 
 
 
 ∫√ 
 
3
2
3
2
 
 
 
 
3
2 
 ( 1,0 PONTO ) 
 b) ∫
 ( 1 √ )
√ 
 
 √ 
 
 √ 
 
 
 ∫ ∫ 
 
 ( 1,0 PONTO ) 
 
 𝑦 ( 𝑠𝑒𝑛 𝑥)√𝑥 [ 
 
 √𝑥
 ( 𝑠𝑒𝑛 𝑥) √𝑥 
 
𝑠𝑒𝑛 𝑥
 𝑥 ] 
𝑓 (𝑥) 𝑥 − 𝑥 
𝑓(𝑥) 
 
 
𝑥 − 
 
 
𝑥 𝑥 − 
𝐼 
 
 
 ( 𝑡𝑔 𝑥 ) 
 
 𝐶 
𝐼 𝑒( √𝑥 ) 𝐶