Let r=5x^(5/2), x greater than 0. Use differentials to estimate the percentage change in r, if x increases by 2%.

Question

hartnn · Answer

1. find dr/dx
2. plug in $\dfrac{dx}{x} = 0.02$

anonymous · Answer

I understood that, but I'm not sure to continue on, and didn't really understand the question exactly...

hartnn · Answer

r is dependent on x as $r = 5x^{5/2}$

so when x increases, 'r' also increases,
makes sense?

hartnn · Answer

the questions asks, 
by how much % does r increase, when x increase by 2%

anonymous · Answer

okay..

hartnn · Answer

note % change in r = dr/r 

anyways, 1st step is to get dr/dx

anonymous · Answer

So we need to take the derivative of 5x^(5/2)?

hartnn · Answer

yes,
that will give you dr/dx

anonymous · Answer

I got this: dr/dx= 25x^(3/2)/2

hartnn · Answer

thats correct.

hartnn · Answer

now we have 
dx/x = 0.02 ---> dx = 0.02x

and remember we need dr/r

hartnn · Answer

dr= [25x^(3/2)/2] *dx 
ok?
now plug in the dx here

anonymous · Answer

So it will be like this:
$$dr=\frac{ 25x^{3/2} }{ 2}(0.02x)$$

hartnn · Answer

yessss


now either divide both sides by 'r' to get dr/r
or realize that there is already r (when you simplify!) on right side..

try dividing r on both sides, so you'll be able to see it

hartnn · Answer

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