Trapezoidal is different because instead of multiplying by delta x, you multiply by delta x/2 and you also have on more term then your number of subintervals.
The formula is : delta x/2 [f(a) + 2f(a + delta x) + 2f(a+ 2 delta x) + ....f(b)]
For this problem: 1/2 [ f(-3) + 2 f(-2) + f( -1)] and then plug in.
Substitution takes the place of the derivative rules for problems such as product rule and quotient rule. The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in
e integration:
whatever is raised to the e power will be your u and du will be the derivative of u. For example:
e^2x-1dx
u=2x-1 du=2
rewrite the function as:
1/2{ e^u du, therefore
1/2e^2x-1+C will be the final answer.
Optimization can be used for finding the maximum/minimum amount of area of something. Steps in order to optimize anything:
1. 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
*Linearization
I'm not quite sure when to do it, i know i'm supposed to do linearization when i see approximate..but i'm not sure how to do it. Is it just finding a slope?
Equation of a tangent line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)
okay so im having trouble with the mram lram and trapezoidal so please help.
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The MRAM, LRAM, Trapezoidal and Midpoint we have been seeing on the AP tests is to determine them from least to greatest. On the last AP, it was said that the graph was increasing and concave up. From that, you can sketch the graph. Once the graph is sketched, draw the bars for each ram. RRAM will start from the right, which is on top of the graph is this case, and go to the left and down therefore it is a over approximation. Left will start at the left and be below the graph this turns out to be a under approximation. If you are like me, I am not quite sure how to draw trapezoidal so I just remember if increasing, trapezoidal is over and if decreasing, trapezoidal is under. From there, you can determine the order.
ReplyDeletedelta x= b-a/number of subintervals
ReplyDeleteLRAM-left hand approximation
delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-right hand approximation
delta x[f(a+delta x)+...f(b)]
MRAM-middle approximation
delta x[f(mid)+f(mid)+...]
Trapezoidal
delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
the only thing i can tell you to do is to just take your time and just plug everything in one step at a time
MRAM you have to take your intervals and just find the middle of each interval and just take it from there
MRAM-middle approximation
ReplyDeletedelta x[f(mid)+f(mid)+...]
LRAM-left hand approximation
delta x[f(a)+f(a+delta x)+...f(b-delta x)]
Trapezoidal
delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
you just basically have to remember them and practice them but with trapezoide you can't forget your delta x and with Mram you have to remember to find the middle of your intervals.
These things are really simple, we just get caught up in everything else and forget about it. Take your time, learn your formulas and the differences between them, then you'll be set and wont have to worry about not knowing it anymore.
ReplyDeletedelta x=b-a/number of subintervals
LRAM-
delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-
delta x[f(a+delta x)+...f(b)]
MRAM-
delta x[f(mid)+f(mid)+...]
Trapezoidal
delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
LRAM- left hand approximation. x[f(a)+f(a+x)+...f(b)]
ReplyDeleteRRAM- right hand approximation. x[f(a+x)+...f(b)]
MRAM- approximation from the middle. x[f(mid)+f(mid)+...]
Trapezoidal- x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
all you've gotta do is plug into these formulas and you're set.
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