Question

If T(44)=17 then find lim(h->0) (T(44+h)-T(44))/h

Answer 1

It was not given... all we got was the table:

x 35 44 53 62 71
T (x) 25 17 15 32 28

Answer 2

I originally put 1 figuring \[\lim_{h \rightarrow 0} \frac{ ((17+h)-17) }{ h } = h/h=1\]

Answer 3

They are essentially asking you to find the slope of T at x = 44.
You can approximate it by assuming a straight line between x = 44 and x = 53.
You can also evaluate it on the left side and perhaps take the average of the two.

Answer 4

ok, thanks!! I think I know what to do from here...

Answer 5

You are welcome.