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Simple calculus limit

  1. Oct 1, 2014 #1
    1. The problem statement, all variables and given/known data
    find the equation of the line perpendicular to the tangent line at the given point f(x)= x√x P(1,1)

    2. Relevant equations
    f(a+h) - f(a) / h

    3. The attempt at a solution
    ok so first i replace (f(a) and f(a+h) in the equation x√x, and then i get

    1. a+h√a+h - a√a / h, then i rationalize the numerator and then i get
    2. a+h)^2(a+h) - a^2(a) / h(a+h)√a+h + a√a

    and if i try expanding this etc i just get indeterminate form.. where did i go wrong ?i still get indeterminate form even after using 1 instead of a
     
  2. jcsd
  3. Oct 1, 2014 #2
    oh and btw i havent learned derivatives, so i have to use limits
     
  4. Oct 1, 2014 #3

    Mark44

    Staff: Mentor

    Your formula needs more parentheses. What you wrote means
    $$f(a + h) - \frac{f(a)}{h}$$
    There need to be parentheses around the entire numerator, like so: (f(a+h) - f(a)) / h
    To look really nice, you can use LaTeX (see https://www.physicsforums.com/threads/physics-forums-faq-and-howto.617567/#post-3977517)

    Both the above are really hard to read, due to many missing parentheses. For one, the entire numerator needs parentheses around it. For another, a + h√a + h doesn't mean what you intend, which is that a + h is multiplying √(a + h). Also, in #2, you are missing a left parenthesis at the beginning of the line.
    Please rewrite the two expressions above so that we can read them.
     
  5. Oct 1, 2014 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    You definitely do NOT want what you wrote, which was
    [tex] f(a+h)- \frac{f(a)}{h}[/tex]
    Can you see how to write things properly?
     
  6. Oct 1, 2014 #5
    ok im sorry lol i didnt know about latex , i got it though so thanks i guess

    i forgot to expand one of my binomials
     
  7. Oct 1, 2014 #6

    Ray Vickson

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    Science Advisor
    Homework Helper

    You do not need LaTeX; you need parentheses, like this: [f(a+h) - f(a)]/h. You need to make sure that when your expressions are read by standard parsing rules they come out saying what you want. Remember: multiplication and division have higher priority than addition and subtraction, etc.
     
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