1)a)f derivat (x) =[tex] e^{x} [/tex] -1
b)f derivat (x)=0⇒[tex] e^{x} [/tex]-1=0⇒[tex] e^{x} [/tex]=1⇒x=0
x | -∞ 0 +∞
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f derivat (x) |-------------------0++++++++++++
______________________________________ ⇒f strict descrescataoare pe
f(x) | scade creste (-∞,0] si strict crescatoare pe
[0,+∞)
2) a)f derivat (x)=1-[tex] \frac{1}{x} [/tex]=[tex] \frac{x-1}{x} [/tex]
f derivat (x)=0⇒x-1=0⇒x=1
x |0 1 +∞ f(1)=1-ln1=1-0=1
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f derivat (x) |----------------0++++++++++
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f(x) | scade 1 creste
c)[tex] \lim_{x \to \infty} \frac{f(x)-x}{x}= \lim_{x \to \infty} \frac{x-lnx-x}{x}= \lim_{x \to \infty} \frac{-lnx}{x}= \lim_{x \to \infty} - \frac{1}{x}=0 [/tex]
