=
So now you can fill in
Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.
When I graph this, as it is going to 1 it looks like it reaches and passes 0.5...
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The point P(1, 1/9) lies on the curve y = x/(8 + x). If Q is the point (x, x/(8 + x)), use a scientific calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x.
(a) 0.5
(b) 0.9
(c) 0.99
(d) 0.999
(e) 1.5
(f) 1.1
(g) 1.01
(h) 1.001
If you could just help me with how to solve these I should be able to work them out myself.
It's a typo: after the "=" sign I forgot to put an extra "x" in the numerator.
It was supposed to be:
Now plug in . It gives
L'hopital -Theorem confirms this:
Second problem: The derivative as I earlier stated gives a formula for the slope of the point: at any point .
. So if you want to know the slope at the point the derivative gives: and the tangent at is given by