Suppose k and l grow at constant rates given by
And
)What is the growth rate of y if
,a 0?

Question

Suppose k and l grow at constant rates given by 
And 
)What is the growth rate of y if 
,a > 0?

Quizplus · Accepted Answer

Using the Quotient Rule of differentiation, we have:
y' = (k/x - l/x^2)' * e^(kx-l/x)
   = (-k/x^2 + 2l/x^3) * e^(kx-l/x) 
Since a > 0 is a constant, we can substitute x = a/u, and we get:
y' = (-ku/a^2u^2 + 2la^3/u^4) * e^(ka/u - l(u/a))
   = (-k/a^2u + 2la^3/u^3) * e^(ka/u - l(u/a))
Now taking the limit as u -> infinity (i.e. as x -> 0), we get:
y' = -k/a^2 * e^(0) = -k/a^2
Therefore, the growth rate of y is constant and equal to -k/a^2.

Suppose K and L Grow at Constant Rates Given by