notebook.community

Edit and run



In [1]:

    
%pylab
%matplotlib inline









    



Using matplotlib backend: MacOSX
Populating the interactive namespace from numpy and matplotlib



In [2]:

    
3**3









    Out[2]:





27



In [3]:

    
3**3.1









    Out[3]:





30.135325698915423



In [4]:

    
3**3.14









    Out[4]:





31.489135652454948



In [5]:

    
3**pi









    Out[5]:





31.54428070019754

Kan definere $f(x) = 3^x$



In [6]:

    
x = linspace(-2,2,200)
y1 = 1.1**x
y2 = 2**x
y3 = 3**x
plot(x,y1,x,y2,x,y3)









    Out[6]:





[<matplotlib.lines.Line2D at 0x10a533198>,
 <matplotlib.lines.Line2D at 0x10a533358>,
 <matplotlib.lines.Line2D at 0x10a533cc0>]



In [7]:

    
x = linspace(-2,2,200)
y1 = 0.8**x
y2 = 0.3**x
y3 = 3**x
plot(x,y1,x,y2,x,y3)









    Out[7]:





[<matplotlib.lines.Line2D at 0x10a5e4710>,
 <matplotlib.lines.Line2D at 0x10a5e48d0>,
 <matplotlib.lines.Line2D at 0x10a5eb940>]

a negativ? Litt mystisk, komplekse tall, la oss helst ikke gjøre dette!



In [8]:

    
x = linspace(-2,2,200)
y = (-3)**x
plot(x,y)









    



/Users/olivier/anaconda/envs/python3/lib/python3.4/site-packages/ipykernel/__main__.py:2: RuntimeWarning: invalid value encountered in power
  from ipykernel import kernelapp as app






    Out[8]:





[<matplotlib.lines.Line2D at 0x10a6e3f98>]

$f(x) = e^x$



In [9]:

    
x = linspace(-2,2,200)
y = exp(x)
plot(x,y)
axis('equal')









    Out[9]:





(-2.0, 2.0, 0.0, 8.0)

$e^{2.4}$ er grensen av $(1+2.4/n)^n$:



In [10]:

    
n = arange(1,5000)
y = (1+2.4/n)**n
plot(n,y)
plot(n,[exp(2.4)]*len(n))









    Out[10]:





[<matplotlib.lines.Line2D at 0x10a807908>]

Potensfunksjoner



In [11]:

    
x = linspace(.3,3,200)
y1 = x**1.2
y2 = x**2
y3 = x**(-2)
plot(x,y1,x,y2,x,y3)









    Out[11]:





[<matplotlib.lines.Line2D at 0x10a6f9828>,
 <matplotlib.lines.Line2D at 0x10a6f9ac8>,
 <matplotlib.lines.Line2D at 0x10a582b38>]



In [12]:

    
x = linspace(.1,3,200)
y = x**0.7
plot(x,y)









    Out[12]:





[<matplotlib.lines.Line2D at 0x10a94b748>]

For noen ok også for $x <0$:



In [13]:

    
x = linspace(-2,2,200)
y = x**(-2)
plot(x,y)









    Out[13]:





[<matplotlib.lines.Line2D at 0x10ac29cc0>]

Potensfunksjoner og eksponentialfunksjoner



In [14]:

    
x = linspace(0,100,200)
y = (x**10)/(1.2**x)
plot(x,y)









    Out[14]:





[<matplotlib.lines.Line2D at 0x10ade5e48>]

Kontinuerlig rentesrente:



In [15]:

    
p = 0.05
t = 6
# årlig rente:
(1+p)**t
# månedlig rente
(1+p/12)**(12*t)
# daglig rente
(1+p/365)**(365*t)
# kontinuerlig:
exp(p*t)









    Out[15]:





1.3498588075760032



In [ ]: