controlemathfonction.py

Created on January 02, 2022
870 Bytes
Ex 1:
  (u*v)'=u'*v+u*v'
f'(x)= e**x  + xe**x     =>   e**x  *(1+x)
e**x > 0                     (1+x)>/0
                              x>/-1
-00     -1      +00 
    -    0   +
    

-00     -1      +00
-1              +00
      -e-1/e

fonction f continue, derivable et strictement croissante sur [0;1] alors ...
Xo=0,57


Ex 2:
  g(x)= -x**2   +1 -lnx

Ax E ]0;+00[, g'(x)= -2x - 1/x       <0 

----

lim 1/x = +00     lim lnx = -00       
P=> lim lnx/x = lim 1/x  * lnx   = -00 




lim x->0  = -00 
av d'eq x=0 

lim x-> +00  =  0 
ah d'eq y=0 en +00





-lnx>/0
lnx</0
x</e**0 = 1


Position relative :   0     1     +00
  -x+2                  -   0   + 
                      dessous        dessus
x->0




1-2e**-x  >/ 0 
1 >/ 2e**-x
1/2 >/ e**-x
ln1/2 >/ -x 



2lnx + 4 >/ 0 
2lnx >/ -4
lnx >/ -4/2 = -2
e**lnx >/ e**-2
x >/ e**-2