Advanced Search

Question: What is wrong with my logic in interpreting this seemingly simply plot.

Question:What is wrong with my logic in interpreting this seemingly simply plot.

zenterix 405 Maple 2022
plot evalf floating-point plotting
April 26 2025
0

I am very confused by the y-value of the rightmost point on the plot below.

restart

I'd like to find the values of x for which x^2/(10^(-8)-x) = 5*10^(-3).

So I ask Maple to solve this equation.

evalf(solve(x^2/(10^(-8)-x) = 5*10^(-3)))

-0.5000010000e-2, 0.10000e-7

 (1)

Do these solutions work?

eval(x^2/(10^(-8)-x), x = 1.0000*10^(-8)) = Float(infinity) 

eval(x^2/(10^(-8)-x), x = -0.5000010000e-2) = 0.5000000000e-2 NULL

Suppose I define the function

f := proc (x) options operator, arrow; x^2/(1/100000000-x) end proc = proc (x) options operator, arrow; x^2/(1/100000000-x) end proc 

f(10^(-8))

Error, (in f) numeric exception: division by zero

  

f(.999999*10^(-8)) = 0.9999980000e-2NULL

f(.99999*10^(-8)) = 0.9999800001e-3NULL

Now, the function seems continuous between these two points

plot(f, .99999*10^(-8) .. .999999*10^(-8))

  

It is late, and perhaps I am just tired and not seeing things clearly. I expected the topmost point on the right to have a y-value of 0.00999998, ie almost 0.01.

I expected that the bottom leftmost point to be 0.0009999800001, ie almost 0.001, and it is.

And I thus expected to show that there must be some x for which we have f(x)=0.005, which if I am not mistaken is between the two numbers. After all, 0.999998e-2-0.5e-2 = 0.499998e-2NULL

0.5e-2-0.9999800001e-3 = 0.4000020000e-2NULL

what am i missing here?


Download plotq.mw
Please Wait...