Related Rates:
1. Identify all variables and equations
2. Identify what you are looking for
3. Make a sketch and label
4. Write an equation involving your variables
5. Take the derivative with respect to time
6. Substitute in derivative and solve.
Example:
Air is being pumped into a spherical balloon at a rate of 4.5 cubic ft/min. Find the rate of change of the radius when the radius is 2 ft.
1. r=2ft; dv/dt = 4.5 ft^3/min
2. NEED TO FIND dr/dt.
3. Volume of sphere: v=4/3 pi r^3
4. derivative: dv/dt = 4 pi r^2 dr/dt
5. Plug in: 4.5 = 4pi(2)^2 dr/dt
6. 4.5=16 pi dr/dt
dr/dt = 9/32 pi ft/min
things i need help with is bacteria problems. I also need help with intergration of trig functions still. I need to start getting these problems right on my ap test
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integration of trig problems are always the opposite of a derivative..so, just do the opposite..
ReplyDeletelike the integral of sin is -cos
.... the ingegral of cos is +sin
and you just go down the list and think "what would be the opposite of the derivative?"
The only thing I can add to Steph's comment is DON'T FORGET THE IDENTITIES!! This messes a lot of people up (guilty)
ReplyDeleteI *think* the ones from Advanced Math still apply here and she gave us a pretty large list of some as well. You might try to memorize those?