alright, spring break is over, and it's back to school!...realizing that we only have a few days left i'm beginning to panic over all of the projects that we have due!!!
OH EM GEE!!
so my spring break was good..i can't complain..and i'm missin it already, but here's what we should know for Calculus:
Monday thru Thursday we will be taking AP Tests and we are not allowed to do Corrections for a perfect score, because corrections will be a grade in themselves!..GOOD LUCK TO EVERYONE!
so lets go over a few things:
LINERAZATION
The steps for working linearization problems are:
1. Identify the equation
2. Use the formula f(x)+f ' (x)dx
3. Determine your dx in the problem
4. Then determine your x in the problem
5. Plug in everything you get
6. Solve the equation
LIMIT RULES ARE A MUST !!!! WE SEE THEM ON EVERYTHING!!!
The limit rules are:
1. if the highest exponent is the same on the top and bottom then the limit is the top coefficient over the bottom coefficient of the highest exponents.
2. If the highest exponent is on the top then the limit is infinity.
3. But if the highest exponent is on the bottom then the limit is 0.
RELATED RATES SHOW UP A LOT TOO..AND THEY TIE INTO A LOT OF THINGS AS WELL:
The steps for related rates are:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
not to mention,.....ANGLE OF ELEVATION:
I'm not very good at those so can anyone explain that
also...OPTIMIZATION:
not so great at those either...HELP please!!
~ElliE~
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Steps in order to optimize anything:
ReplyDelete1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is usually the other equation that ties in all the information given in the problem.
2. Solve the secondary equation for one variable and then plug that variable back into the primary. If the primary equation only have one variable you can skip this step.
3. Take the derivative of the primary equation after plugging in the variable, set it equal to zero, and then solve for the variable.
4. Plug that variable back into the secondary equation in order to solve for the last missing variable. Check endpoint if necessary to find the maximum or minimum answers.
Optimization
ReplyDeleteThe steps are:
1. Determine everything given in the problem and what you are looking to maximize or minimize. This is stated in the problem.
2. Write a primary equation, which is an equation for what you are maximizing or minimizing.
3. Write a secondary equation using the other information given.
4. Solve the secondary equation in terms of one variable (if necessary) then plug that into the primary equation for that variable.
5. Take derivative of the plugged in primary equation, set the equation equal to zero, then solve for the remaining variable.
6. Plug back into the secondary equation to find the other variable.
EXAMPLE:
We need to enclose a field with a fence. We have 500 feet of fencing material and a building on one side of the field so won't need any fencing. Determine the dimensions of the field that will enclose the largest area.
1. P=500 ft, one side does not need fencing, maximizing area (enclose the largest area)
2. Since we are maximizing area, the primary equation will be the area equation for a rectangle. A=xy
3. The secondary equation will be perimeter since that is given in the problem. 500= x+2y
Note: the formula for perimeter is usually 2x+2y, but since one side does not need fencing, it is only x+2y.
4. Solve for one variable: 500=x +2y x= 500 -2y
Now plug into primary equation: A= 500 - 2y (y)
Distribute the y in: 500y - 2y^2
5. Take derivative: 500 - 4y
Set equal to zero and solve for y; 500 -4y = 0 y = 125
6. Plug y into secondary equation to find x: 500 = x + 2y 500 = x+2(125) x= 250
The dimensions of the largest area are 250 X 125
The rules to optimize anything are . first u must identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is usually the other equation that ties in all the information given in the problem. Then solve the secondary equation for one variable and then plug that variable back into the primary. If the primary equation only have one variable you can skip this step. Then take the derivative of the primary equation after plugging in the variable, set it equal to zero, and then solve for the variable. Then you plug that variable back into the secondary equation in order to solve for the last missing variable. Check endpoint if necessary to find the maximum or minimum answers.
ReplyDelete