Question

Se considera functia f:R-> R,[tex] a ∈ R

a) Calculati f(-2)-f(-1)

b) Calculati \lim_{x \to \infty} \frac{f(x)+x}{ x^{2} +x}
[tex] \lim_{x \to \infty} \frac{f(x)+x}{ x^{2} +x}
[/tex]

Answer 1

a) f(-2)=e^(-2)-1=1/e^2-1
f(-1)=e^(-1)-1 =1/e-1
f(-2)-f(-1)=1/e^2-1-1/e+1=1/e^2-1/e
b)lim[f(x)+1]/(x²+x)=lim(x²+x+a+x)/(x²+x)=lim(x²+2x+a)/(x²+x)=1  Pt ca   gradul  numaratorului = gradul  numitorului