Question

Am nevoie de ajutor la problema 381. Mulțumesc!

Answer 1

f''(x) = 1/x

∫f''(x)dx = ∫(1/x)dx

f'(x) + C₁ = lnx+C₂

f'(x) = lnx+C

f'(1) = 0 => ln1+C = 0 => C = 0

=> f'(x) = lnx

∫f'(x)dx = ∫(lnx)dx

f(x)+C₁ = xlnx-x+C₂

f(x) = xlnx-x + C

f(1) = 0 => 1ln1 - 1 + C = 0 => C = 1

=> f(x) = xlnx-x+1

Răspuns corect, alt răspuns.