Question

exercitiul 21 va rog dau coroana​

Answer 1

Răspuns:

Explicație pas cu pas:

a) lim x->inf(√x -lnx) =

lim x->inf(ln(e^√x) - lnx)) =

lim x->inf(ln((e^√x)/x)) = inf

( e^√x creste mai repede decat x)

b) lim x->0 (√x -lnx) =

lim x->0 (ln((e^√x)/x)) = e^0/0 = 1/0 = inf

Asimpt. vert. x = 0

lim x->inf(f(x)/x) = 0

Nu are asimpt. oblica

c) f'(x) = 1/(2√x) -1/x =

(x - 2√x)/(2x√x)

f'(x0 = 0,  x - 2√x=0,  

x = 2√x,  x^2 = 4x,   x = 4

f(4) = 2 -ln4

Punct de minim: (4; 2-ln4)