Question

Buna seara!
Va rog sa ma ajutati si pe mine la matematica bac Tip sub 3.
Ex:1 si 2 punctele a si c ​

Answer 1

1.

a)

$f'(x)=(lnx-\frac{1}{x})'=\frac{1}{x}+\frac{1}{x^2}=\frac{x+1}{x^2}$

c) ecuatia tangentei in x₀=1

y-f(x₀)=f'(x₀)(x-x₀)

y-f(1)=f'(1)(x-1)

$f'(1)=\frac{1+1}{1} =2$

$f(1)=ln1-\frac{1}{1} =0-1=-1$

ecuatia tangentei:

y-(-1)=2(x-1)

y+1=2x-2

y=2x-3

2.

a)

$\int\limits^1_0 {e^x} \, dx =e^x|_0^1=e^1-e^0=e-1$

c)

$\int\limits^1_0 {e^x-\frac{x^2}{2}-1 } \, dx =e^x|_0^1-\frac{1}{2}\times\frac{x^3}{3} |_0^1-x|_0^1=e-1-(\frac{1}{6}-0)-(1-0)=e-1-\frac{1}{6} -1=\frac{6e-13}{6}$