1.
a)
[tex]\lim_{x \to 3} \frac{x-1}{x-2} =\frac{3-1}{3-2}=2[/tex]
c)
y-f(3)=f'(3)(x-3)
[tex]f(3)=\frac{3-1}{3-2} =2[/tex]
[tex]f'(3)=-\frac{1}{(3-2)^2} =-1[/tex]
y-2=-1(x-3)
y-2=-x+3
y=-x+5
2.
a)
[tex]\int\limits^1_{-1} {2x+1} \, dx=(x^2+x) |_{-1}^1=2-0=2[/tex]
c)
[tex]F(x)=\int{f(x)} \, dx[/tex]
[tex]F(x)=\frac{x^3}{3} +x^2+x[/tex]
Ca sa studiem monotonia trebuie sa calculam derivata
F'(x)=f(x)
f(x)=x²+2x+1=(x+1)²≥0⇒ f crescatoare pe R
