Question

Am nevoie de ajutor la subiectul 3 (Ex1/2 a si c )
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Answer 1

1.

a)

$\lim_{x \to 3} \frac{x-1}{x-2} =\frac{3-1}{3-2}=2$

c)

y-f(3)=f'(3)(x-3)

$f(3)=\frac{3-1}{3-2} =2$

$f'(3)=-\frac{1}{(3-2)^2} =-1$

y-2=-1(x-3)

y-2=-x+3

y=-x+5

2.

a)

$\int\limits^1_{-1} {2x+1} \, dx=(x^2+x) |_{-1}^1=2-0=2$

c)

$F(x)=\int{f(x)} \, dx$

$F(x)=\frac{x^3}{3} +x^2+x$

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