lista - aplicações de derivada.pdf

7/17/2019 Lista - Aplicações de Derivada.pdf

http://slidepdf.com/reader/full/lista-aplicacoes-de-derivadapdf 1/5

2012.1

t

f (t) = 16t + t2

0 ≤ t ≤ 8

[b, b + h], 0 ≤ b < 8

[3;3, 1], [3;3, 01] [3;3, 001]

t

t = 3

t

y = b

t + ct y t

t = 2?

x

x = 3t2 − t3

x

t

4

4

4

W (t) =

20 + 1

2(t + 4)2, 0 ≤ t ≤ 60

24, 4t + 604, 60≤

t≤

90,

t

t = 50

51

t = 80

90.000

t

2500t2

[2, 5]

2



x

x = 3 + 2t − t2, t ≥ 0

t

t

v(t)

x

x = −t3 + 3t2, t ≥ 0

v(t)

a(t)

limt→∞(−t3 + 3t2)

x =

−t3 + 3t2, t

≥0

P

y = 3x2 − 2x

x(t)

y(t)

P

dx

dt = 0 y P

x

P

P

y =

1

x2 + 1

x

5(m/s)

y

x = 10

a)f (x) = 2x − 1 b)f (x) = 3x2 + 6x + 7

c)f (x) = (x − 1)(x − 2)(x + 3) d)f (x) = x

2 + sin x

e)f (x) = e−x f )f (x) = x2

x − 1

g)f (x) = ex sin x, x ∈ [0, 2π].

a)f (x) = 3x2 + 6x + 1 b)f (x) = 4x3 − 8x2

c)f (t) =

t

−1

t + 1 d)f (x) = |2 − 6x|

e)f (x) =

x + 4, x ≤ 2x2 − 2, x > −2

f )f (t) =

3 − 4t, t > 04t + 3, t ≤ 0

g)f (x) =

1 + x, x < −11 − x2, x ≥ −1

h)f (x) =

10 − (x − 3)2, x ≤ −25(x − 1), −2 < x ≤ −1

− 91 + (x − 2)2, x > −1h)f (x) = 7x2 − 6x + 3 b)f (x) = 1

3x3 + 3x2 − 7x + 9

i)f (x) = 1

4x4 − 5

3x3 + 4x2 − 4x + 8 d)f (t) =

t2, t < 03t2, t ≥ 0

j)f (x) = 3 + (2x + 3)43 f )f (x) =

x + 1

x2 − 2x + 2

k)f (x) = x2√

16 − x



y = logax

x x = e

a > 1

a

b

f (x) = x3

+ ax2

+ b

(−2, 1)

a,b,c d f (x) = 2ax3 + bx2 − cx + d x = 0

x = 1

a > 0

a)f (x) = −x3 + 5x2 − 6x b)f (x) = 3x4 − 10x3 − 12x2 + 10x + 9

c)f (x) = 1

x + 4 d)f (x) = 4

√ x + 1 −

√ 2

2 x2 − 1

e)f (t) = t2 + 9

(t − 3)2 f )f (t) = e−t cos t, t ∈ [0, 2π]

g)f (x) =

x2 − 4, x ≤ 24 − x2, x > 2

a)f (x) = x3 − 3x2 + 1 b)f (x) = x + 1

x c)f (x) = x2 + 1

x

d)f (x) =

x

1 + x2 e)f (x) = e2x

− ex

f )f (x) = e

1x

g)f (x) = x3 − x2 + 1

x h)f (x) =

3x2 + 4x

1 + x2 i)f (x) = −x4 + 4x3 − 4x2 + 2

j)f (x) = x2 − x + 1

2(x − 1)

l

l

a

A B

l



375

2

3, 5

2 2 2, 5

400 2

a b a

400

2

a b

9

12



a)limx→−14x3 + x2 + 3

x5 + 1 b)limx→1

x100 − x2 + x − 1

x10 − 1 c)limx→0+ xe

1x

d)limx→+∞e3x

x2 e)limx→+∞

lnx

e3x f )limx→0+ sin x ln x

g)limx→0+(1 − cos x) ln x h)limx→+∞(x2 + 1) 1lnx i)limx→0+

1

x + ln x

j)limx→0−(1 − cos x)1x l)limx→0

tg3x − sin x

sin3 xm)limx→0

sec3 x

1 − cosx

n)limx→+∞ x3e−4x o)limx→+∞

x − 3√

x3 − x

p)limx→1−e

1

x2−1

x − 1

q )limx→+∞

x

x2 + 1

x

f (x) = x2 sin 1x

g(x) = x limx→0 f (x) = limx→0 g(x) = 0 limx→0 f (x)g(x) = 0

limx→0

f

(x)

g

(x) 1

lista - aplicações de derivada.pdf

Documents