Question

Consider the function f(x)=x-1/x-2
(a)set up the equation for the derivative of f at the point (5,4/3) using the f1(x)lim w approaches x f(w)-f(x)/w-x

Answer 1

\[\lim_{w\to 5}\frac{\frac{w-1}{w-2}-\frac{4}{3}}{w-5}\]

Answer 2

answer is x=-1/2

Answer 3

computing it is a different story, but not that hard
do the algebra in the numerator and then you will be able to cancel the \(w-5\) in the denominator

Answer 4

How would I go about evaluating it

Answer 5

algebra

Answer 6

forget the \(w-5\) in the denominator, and compute
\[\frac{w-1}{w-2}-\frac{4}{3}\]

Answer 7

you get
\[\frac{3(w-1)-4(w-2)}{3(w-2)}\] leave the denominator in factored from, simplify the numerator

Answer 8

a miracle occurs and you get
\[\frac{5-w}{3(w-2)}\]

Answer 9

NOW ( and only at this step ) recall that you are dividing this whole mess by \(w-5\) which cancels with the \(5-w\) up top, leaving behind a \(-1\) in the numerator, for a total of
\[\frac{-1}{3(2-2)}\]

Answer 10

oops i meant
\[\frac{-1}{3(w-2)}\]

Answer 11

and now you are free to take the limit by replacing \(w\) by \(5\)

Answer 12

Oh ok that makes sense thanks a bunch you explained it much better than my teacher :)

Answer 13

notice that it is all algebra, so you need to be confident in your algebra ability. it should always work out that you can cancel the factor that would get you zero in the denominator, so you can take the limit by direct substitution

yw

Answer 14

its all about how you can use techniques to twist the equations to get it into forms that are more suitable for taking out limits