E is a vectorial plan in R with a base
B=(i^→ ,j^→ ). f is an endomorphism of E
defined ∀ u^→ =xi^→ +yj^→ by f(u^→ )=(−7x−12y)i^→ +(4x+7y)j^→ .
1) Determinate f(i^→ ) and f(j^→ ) then
write the matrice of f in (i^→ ,j^→ )base.
Consider the functionf defined by parf(x) = −x + ((ln x)/x) in the interval
: ]0,+∞[. (C_f ) is its representative curve in an orthonormal
reference system (O,i^→ ,j^→ ).
Calculate lim_(x→0^+ ) f(x), lim_(x→+∞) f(x).
A primitive of the function defned by f(x) = x −1 + (1/(x+1)) is
A. F(x) = (x^2 /2) −x + ln(x + 1) B. F(x) = (x^2 /2) + ln(x−1)
C. F(x) = (x^2 /2)−x + ln(1−x) D. F(x) = −x + ln(x−1)