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Slope of curve

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Question: Find the slope of the curve at the indicated point.

    y= (1/x-1) at x=2


    2. Relevant equations
    Don't know what relevant questions mean.


    3. The attempt at a solution
    (y(x+h) - y(x))/(x+h)-h
    ( (1/x-1 + h) - (1/x-1) )/h
    ( (1/2-1 + h) - (1/2-1) )/h
    ( (1+h) - (1) )/h
    h/h=1

    the problem is the book says it should be -1.
    Help anyone?
     
  2. jcsd
  3. Mar 28, 2012 #2
    You need to be careful when writing math online. What you wrote as y= (1/x-1) implies [itex]y = \frac{1}{x} - 1[/itex]. I suspect you meant to write [itex]y = \frac{1}{x-1}[/itex] as that function gives the correct answer.

    You plugged in values wrong right from the start which is why your answer is wrong. Let's rewrite your function as [itex]f(x) = \frac{1}{x-1}[/itex]. Now you need to compute [itex]\displaystyle\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}[/itex]. Now, what does [itex]f(x+h)[/itex] equal? Remember, you need to plug in the value (x+h) where ever you see an x.
     
  4. Mar 28, 2012 #3
    I made a mistake on the tex look at the next reply.
     
  5. Mar 28, 2012 #4
    Well this question is fairly simple, all you have to do is take the derivative of the equation:

    [tex]f(x)=\frac{1}{x-1}[/tex] and then calculate the limit:

    [tex]\lim_{x\rightarrow2}f'(x)[/tex] and you should get the same answer that your textbook has.

    Ps: the derivative is the slope of the tangent line at a certain point.
     
  6. Mar 28, 2012 #5
    could you guys tell me what you are using to make the fractions look like that? So no one gets confused?
     
  7. Mar 28, 2012 #6
    We are using a code called LaTeX, it makes all the math look pretty and readable.

    I can give a quick little tutorial for fractions but to learn everything I'll redirect you to a website.

    So, first of all, you must use TAGS to show that you want to type in code. The tags are
    Code (Text):
    [itex][/itex]
    . Everything between the tags will be put into code. What's nice about this forum is that if you see a pretty looking formula that was coded in LaTeX, you can right click on it and select Show Math As -> TeX commands to see what the code is. Try it out for ours above.

    For basic fractions the code is
    Code (Text):
    [itex]\frac{a}{b}[/itex]
    which will look like: [itex]\frac{a}{b}[/itex]. Everything you put in the first set of brackets will go in the numerator, everything in the second will go in the denominator. You can even do fractions in fractions:
    Code (Text):
    [itex]\frac{\frac{c}{d}}{b}[/itex]
    = [itex]\frac{\frac{c}{d}}{b}[/itex].

    To learn more if you want, try these two sites out:

    http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols [Broken]
    http://detexify.kirelabs.org/classify.html
     
    Last edited by a moderator: May 5, 2017
  8. Mar 29, 2012 #7
    k thnks and btw i got the answere :D
     
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