(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a worked example from Stewart's Early Transcendentals 6e section 2.7 p. 145 for anybody curious.

Let [tex]f(x)= \frac{3}{x}[/tex]. Find an equation of the tangent line to the hyperbola at point (3,1).

2. Relevant equations

[tex]m = \lim_{h\rightarrow 0}\frac{f(a+h) - f(a)}{h}[/tex]

3. The attempt at a solution

His solution goes as such:

1) [tex]m = \lim_{h\rightarrow 0}\frac{f(3+h) - f(3)}{h}= \lim_{h\rightarrow 0}\frac{\frac{3}{3+h} -1}{h}[/tex]

Plug in the point coordinates into the equation and evaluate.

2) [tex]\lim_{h\rightarrow 0}\frac{\frac{3-(3+h)}{3+h}}{h}[/tex]

Consider the 1 as 1/1, cross multiply and multiply through the denominator. The reverse of partial fraction decomposition (recomposition?)

3) [tex]\lim_{h\rightarrow 0}\frac{-h}{h(3+h)}[/tex]

This is where I become confused. Do you have to distribute the negative sign such that 3-(3+h) = 3-3-h = -h?

4) [tex]\lim_{h\rightarrow 0}-\frac{1}{3+h}=-\frac{1}{3}[/tex]

I would have gotten 1/3 instead of -1/3 so I would have made a mistake between steps 2 and 3.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Worked example of a limit

**Physics Forums | Science Articles, Homework Help, Discussion**