Question

If dy/dx=1/x, then the average rate of change of y with respect to x on the closed interval [1, 4] is

a) -1/4
b) (1/2)*ln(2)
c) (2/3)*ln(2)
d) 2/5
e) 2

Answer: C

Answer 1

@eliassaab @thomaster @ganeshie8

Answer 2

@whpalmer4 @AravindG

Answer 3

@kirbykirby @dumbcow

Answer 4

if \(\frac{dy}{dx}=\frac{1}{x}\) then \(y=\ln(x)+c\)

Answer 5

\[\frac{\ln(4)-\ln(1)}{4-1}=\frac{\ln(4)-0}{3}=\frac{\ln(4)}{3}\]

Answer 6

Thank you everyone!

Answer 7

\[\frac{dy}{dx}=\frac{1}{x}\]

\[dy=\frac{1}{x}dx\]

\[\int dy=\int\frac{1}{x}dx\]
\[\int\limits_{0}^{y}dy=\int\limits_{1}^{4}\frac{1}{x}dx\]
\[y=ln(x)|_1^4\]
\[y=ln(4)-ln(1)\]
\[y=ln(2^2)-0\]
\[\boxed{\boxed{y=2ln(2)}}\]

Answer 8

Thank you for the help!