Question

sall ma puteti ajuta va rog sub3 ex 1 ab

Answer 1

f(x)=lnx-1\x
f(x)^=x+1\x²,x∈(0,+∞)
f(x)^=(lnx-1|x)^
(lnx)^=1\x
(1\x)^=-1|x²
1\x+1\x²=x+1\x²
f(x)^=x+1\x²⇒(A)⇒x∈(0,+∞)

b)lim f(x)-f(2)\x-2=3\4
x⇒2

limf(x)-f(a)\x-a⇒f(a)^
x⇒a
f(x)^=x+1\x²⇒f(2)^=2+1\2²⇒f(2)^=3|4  (A)
succes
^⇒derivat
nu am gasit alt semn!

Answer 2

a)f(x)'=$\frac{1}{x}+ \frac{1}{x^2}= \frac{x+1}{x^2}$. b)Conform definitiei, limita respectiva este valoarea derivatei in punctul x=2, deci f'(2)=$\frac{2+1}{2^2}= \frac{3}{4}$