pez_toapanta_t11

1. UNIVERSIDAD DE LAS FUERZAS ARMADAS “ESPE”
NOMBRES: Rosero Steven , Lopez Brayan, Toapanta Anahi
NRC:1911
FECHA :31/10/2017
TALLER 1 DE FISICA
demostrar mediante la definicion de la derivada f(x) = cos(x)
f´´(x) = −sen(x)
lim
∆x→0
f(x + ∆x) − f(x)
∆x
lim
∆x→0
cos(x + ∆x) − cos(x)
∆x
lim
∆x→0
cos(x)cos(∆x) − sen(x)sen(∆x) − cos(x)
∆x
lim
∆x→0
cos(x)cos(∆x) − cos(x) − sen(x)sen(∆x)
∆x
lim
∆x→0
cos(x)cos(∆x) − cos(x) − sen(x)sen(∆x)
∆x
lim
∆x→0
cos(x)(cos(∆x) − 1) − sen(x)sen(∆x)
∆x
lim
∆x→0
cos(x)
(cos(∆x) − 1)
∆x
− sen(x)
sen(∆x)
∆x
lim
∆x→0
(cos(∆x) − 1)
∆x
= 0
lim
∆x→0
sen(∆x)
∆x
= 1
lim
∆x→0
cos(x + ∆x) − cos(x)
∆x
= −sen(x)
f(x) = xn
f (x) = lim
∆x→0
(x + x) − xn
x
(x + ∆x)n
=
n
0
Xn
+
n
1
Xn−1
∆x +
n
2
Xn−2
∆x2
+ ...... +
n
n
∆xn
f (x) = lim
∆x→0
n
0 Xn
+ n
1 Xn−1
∆x + n
2 Xn−2
∆x2
+ ...... + n
n ∆xn
− xn
x
1

2. f (x) = lim
∆x→0
nXn−1
+
n
2
Xn−2
∆x + ...... + ∆xn−1
f (x) = nXn−1
f(x) = ax
In[f(x)] = In(ax
)
In[f(x)] = xIn(a)
1
f(x)
[f (x)] = x In(a)
f (x)
x
= f(x)In(a)
df
dx
= ax
In(a)
ACTIVIDAD NUMERO 2
f(x) = A0e(x2
+b)
si A0, b R
f (x) = A0e(x2
+b)
(2x)
f (x) = 2A0xe(x2
+b)
f(x) = 5sen(5x − 3)
f (x) = 5cos(5x − 3) ∗ 5
f (x) = 25cos(5x − 3)
f(x) = 4
√
x − 6
x
2
3
f (x) = 4 ∗
1
2
x− 1
2 − 6(x− 5
3 )
f (x) = 2x− 1
2 − 4x− 5
3
f(x) = (1−cos(4x))2
(1+sen(5))3
f (x) =
g(x)
h(x)
f (x) =
g (x)h(x) − h(x)g(x)
[h(x)]2
2

3. f (x) =
(1 − cos (4x))
2
(1 + sen (5x)) − (1 + sen (5x))
3
(1 − cos (4x))
2
(1 + cos (5x))
3
2
15sen (5x) (−cos (4x) + 1)
2
+ 4 (cos (5x) + 1) (2sen (4x) − sen8x)
(1 + cos (5x))
4
3