<p>A lot of the Euler’s method problems I’ve seen are no calculator. And they’re about the most difficult calculations you have to do without a calculator (and they’re usually not too bad at all).</p>
<p>What can you do with a calculator?
Calculate derivative at a point ( MATH 8 on TI-83/84 )
Calculate a definite integral. ( MATH 9 on TI-83/84 )
Solve an equation ( f(x)=0 at x=? ) - includes finding intersections ( f(x)=g(x) at x=? )
View a graph on your calculator ( y= )</p>
<p>And of course all of your basic stuff (addition, subtraction, multiplication, …)</p>
<p>*Note for 1 + 2: For FRQ’s, don’t forget to write f’(5)=answer, or [Definite integral] f(x)dx=answer. In other words, don’t just write the answer and circle it.</p>
<p>Polar equations can be on the non-calculator section - however, for example, instead of asking you to find the area, the may ask find the integral that would find the area (so you would not be calculating the area yourself).</p>
<p>Also, about your problem with your minor errors, don’t get too worried. You won’t lose a ton of points (sometimes just minus one) depending on what you do. And let’s say you get the wrong answer in part A that you use in part B. Even if you got part A wrong, but you did everything else right in part B (except for using the correct value from A), you’ll get full credit for B.</p>
<p>Hopefully that cleared up a lot of stuff. Look up some sample FRQ from the collegeboard website to see how they’re graded.</p>
<p>ChemE14, thanks so much! That makes me feel a lot better about my study habits. However, I was also referring to messing up on the multiple choice questions. A worst case scenario for me is not getting any answer choices- another is worst case is then getting one and proceeding as if it were right. Thanks!</p>
<p>Also, what identities/derivatives/integrals must we know cold?
I asked a girl in BC Calculus (I took the class last year) and she told me only sinx, cosx, tanx for trig and lnx. Also, to forget the cos2x double identities! Is that really true? I took the PR AB test and found a question asking for derivatives of sec^2x… oh boy.</p>
<p>What must we know cold, if not all of them?</p>
<p>Derivatives of regular and inverse.<br>
Integrations of regular trig.<br>
Integrations of specific forms that will lead to an inverse trig answer (like du/(a^2+u^2) leads to (1/a)(Arctan u/a)).<br>
Power-reducing identities, for the integration of (cos x)^2 and (sin x)^2.<br>
Double angles are useful, but they aren’t a major player.</p>
<p>If you’re working a multiple choice answer and you don’t get any of their choices, I’d consider it a good thing. The wrong choices are usually the result of common errors. And if you are getting the wrong answers, then the only thing you can do is practice and make sure you don’t make the same type of mistakes.</p>
<p>Other things to know: Recognize McLaurin series for cos x, sin x, e^x</p>
<p>On the derivative of sec^2 x (if I read it right):
Rewrite/think of it as (sec x)^2
Power rule –> (2 sec x) * (sec x tan x) = 2 sec^2 x tan x</p>
<p>The integral of the square root of x²-2x+1 from 0 to 1 is .5, but if you do it by hand, you get -.5. This was a question on the non-calculator section. </p>
<p>∫(x²-2x+1)^.5 from 0 to 1
∫[(x-1)²]^.5 from 0 to 1
∫(x-1) from 0 to 1
∫.5x²-x from 0 to 1
.5(1)-(1)-[.5(0)-(0)]
.5 - 1 - 0 + 0 = -.5</p>
<p>What am I doing wrong? =( </p>
<p>Sorry if the work is hard to understand. It’s so much easier to show work through writing.</p>
<p>Don’t simplify the integral. Use substitution when you get to step 2.</p>
<p>∫(x²-2x+1)^.5 from 0 to 1
∫[(x-1)²]^.5 from 0 to 1
u=x-1 du=dx
∫u from 0 to 1
∫(u^2)/2 from 0 to 1
Sub x-1 back in
∫((x-1)^2)/2 from 0 to 1
((1-1)^2)/2
((0)^2)/2-((1)^2)/2=-1/2</p>
<p>I think you need absolute value there because you are getting rid of the square root which would have automatically made it positive…add absolute value to it and you should get the right answer.</p>
<p>Most of the Trap and Riemann problems are unable to be solved with any formulas or programs. They’re usually given in the form of a table with x and f(x). Then they ask you for a trap or a left/right Riemann based on the table.</p>
<p>^Yeah I’ve seen a lot of old FRQ’s with tables that ask for Riemann sum. I think a table is easier than when they just give you a function and an initial condition</p>
<p>I think that formulas are useless with the tables. I think the concepts of left, right, midpoint, and trap sums are what’s going to help you get the questions right, not formulas.</p>
<p>Let y = f(x) be the solution to the differential equation dy/dx = x - y - 1 with the initial condition f(1) = -2. What is the approximation for f(1.4) if Euler’s method is used, starting at x = 1 with two steps of equal size?</p>
<p>The answer is supposed to be -1.24, but I don’t know how please help</p>
<p>So, you need 2 steps, each with delta x being +.2.</p>
<p>First Step: You have the initial point (1, -2)
So, Y=f(1.2)=-2+(2)(.2)=-1.6
This means that there is the point (1.2, -1.6), which you’ll use for the second step.</p>
<p>Second Step: You have the point (1.2, -1.6)
So, Y=f(1.4)=-1.6+(1.8)(.2)=-1.24
This means there is the point (1.4, -1.24). That’s how you get -1.24.</p>