Aulas Praticas Calculo Diferencial E Integral

1

UNIVERSIDADE FEDERAL DE SANTA CATARINA
CAMPUS DE JOINVILLE
EMB 5001 – CÁLCULO DIFERENCIAL E INTEGRAL I
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Unidade 1
Funções reais de variável real e funções elementares do cálculo
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1 – Seja f ( x) 

x2  4
, mostrar que: x 1

(a) f (0)  4
(b) f (2)  0
(c) f (1 / t ) 

1  4t 2 t t2

x 2  4x x 3
15
(e) f (1 / 2) 
2

2
(f) f (t ) 

(d) f ( x  2) 

t4  4 t 2 1

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3x  1
, mostrar que: x7 5 f ( 1)  2 f (0)  3 f (5)
263

7
98
 f (1 / 2)2  1
9
9x  7 f (3 x  2) 
3x  9
 22t 2  38t  88 f (t )  f ( 4 / t ) 
 7t 2  53t  28

2 – Se f ( x) 
(a)
(b)
(c)
(d)

f ( h )  f ( 0)
20
 h 7h  7 
11
(f) f  f (5) 
7
(e)

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3 – Se f ( x) 

ax  b e d   a , mostre que f ( f ( x))  x . cx  d

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4 – Dada ( x) 

1 x 1
, forme as expressões  (1 / x) e
.
(x )
2x  7

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5 – Dada a função f ( x)  x 2  1 , mostrar que, para a  0 , f (1 / a ) 

f (a)
.
a2

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6 – Dada a função f ( x)  1 / x , mostrar que f (1  h)  f (1) 

h
.
1 h

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7 – Seja f ( x)  x  28  x  para 2  x  8 .
(a) Determinar f (5) , f (1 / 2) e f (1 / 2) .
(b) Qual o domínio da função f (x) ?
(c) Determinar f (1  2t ) e indicar o domínio.
(d) Determinar f  f 3 e f  f