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?
- State the slope formula: (y2-y1)/(x2-x1)
- Put the time you need to find into parenthesis or brackets: [0, 5] These are your two x’s.
- Plug x1 into your formula: y=93+2.3(0)^2 = 93 93 is your y1
- Plug x2 into your formula: y=93+2.3(5)^2=150.5 150.5 is your y2
- Plug back into your slope formula: (150.5-93)/(5-0)
- Simplify: 11.5 miles per hour
We can just use the same one for instantaneous speed.
- What is the instantaneous speed for t=3?
State the Instantaneous Speed formula:
Lim f(t-h)-f(t)
H->0 h - In the original problem, replace y with f(t): f(t)=93+2.3(t)2
- Plug in: Lim 93+2.3(3-h)^2-93+2.3(3)^2
H->0 h - Foil the parenthesis:
Lim 93+2.3(9-6h+h^2)-93+2.3(9)
H->0 h - Simplify:
Lim (93+20.7 –13.8h+2.3h^2) – (93 + 20.7)
H->0 h - Once you get it in it's simplest form, plug in for h.
Lim 2.3(0)+27.6
H->0 - 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.
Wow, thanks for clarifying my made-up problem for us :D
ReplyDeleteGlad someone finds my work intriguing!
Also, can you teach me the art of copy-pasting? Thank you!
Ok, for this question you have to use the graph and the piecewise
ReplyDeleteFor 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).
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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