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

Question

Hadley Andrews

Mathematics

26 May, 16:56

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

+2

Answers (1)

Know the Answer?

Gilberto Bartlett · Answer 1

The first thing to do here is to integrate the ordinary differential equation dy/dx = 1/x. This is equal to y = ln x + C. Assuming C is zero. y = lnx. substituting the two interval,

y1 = 0 y2 = ln 4

the rate of change then is equal to (ln4 - 0) / (4-1) equal to 2/3 ln 2. Answer is C

If dy/dx=1/x, then the average rate of change of y with respect to x on the closed interval [1, 4] isa) - 1/4b) (1/2) * ln (2)c) (2/3) * ln (2)d) 2/5e) 2

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