Sunday, October 11, 2009

I'll just go over Instantaneous and average speed since no one seems to really have done that yet.

A wolf runs at y=93+2.3(t)^2 miles in t hours. What is it’s average speed during the first 5 seconds?

  1. State the slope formula: (y2-y1)/(x2-x1)
  2. Put the time you need to find into parenthesis or brackets: [0, 5] These are your two x’s.
  3. Plug x1 into your formula: y=93+2.3(0)^2 = 93 93 is your y1
  4. Plug x2 into your formula: y=93+2.3(5)^2=150.5 150.5 is your y2
  5. Plug back into your slope formula: (150.5-93)/(5-0)
  6. Simplify: 11.5 miles per hour

    We can just use the same one for instantaneous speed.
A wolf runs at y=93+2.3(t)^2 miles per hour.
  1. What is the instantaneous speed for t=3?
    State the Instantaneous Speed formula:
    Lim f(t-h)-f(t)
    H->0 h
  2. In the original problem, replace y with f(t): f(t)=93+2.3(t)2
  3. Plug in: Lim 93+2.3(3-h)^2-93+2.3(3)^2
    H->0 h
  4. Foil the parenthesis:
    Lim 93+2.3(9-6h+h^2)-93+2.3(9)
    H->0 h
  5. Simplify:
    Lim (93+20.7 –13.8h+2.3h^2) – (93 + 20.7)
    H->0 h
  6. Once you get it in it's simplest form, plug in for h.
    Lim 2.3(0)+27.6
    H->0
  7. ANSWER: 27.6 miles per hour.

For what i don't understand..i thought i understood limits, but idk what my deal is this week.
When it says is the limit of f(x) or f(2) larger.. what exactly am i doing.. i think
its one of the first questions on the ch. 1 study guide.

3 comments:

  1. Wow, thanks for clarifying my made-up problem for us :D
    Glad someone finds my work intriguing!
    Also, can you teach me the art of copy-pasting? Thank you!

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  2. Ok, for this question you have to use the graph and the piecewise

    For f(x) and x approaches 1, you use your chart to see what the y value is as it approaches x=1, when you look on your graph, the answer is 2

    For f(2), you have to use the piecewise. You plug 2 into the equation that has 2 is either less than or equal to x. The equation is x-1. Plug 2 into this, and it gives you 1, therefore your answer is f(x) is greater than f(2).

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  3. For your limit question you look into what is given. For f(x) you use your chart to see what it is approaching. For f(2) you use the piecewise. Plug 2 into the equation that has 2 is less than or equal to x. You find that f(x) approaches a bigger number than f(2) therefore making that your answer.

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