<p>Hmm can someone assist me with a question</p>
<p>A function f has Maclaurin series given by (x^4)/2! + (x^5)/3! + (x^6)/4! + … + x^(n+3)/(n+1)!. Which of the following is a expression for f(x)
A) (-3x)(sinx) + 3x^2
B) -cos(x^2)
C) (-x^2)(cosx) + x^2
D) (x^2)(e^x) - x^3 - x^2
E) e^(x^2) - x^2 - 1</p>
<p>Answer is D.
The simple way of getting this problem is looking at the first term that comes up, which is x^4. That means that the first, second, and third derivatives all have to equal 0 at f^(n) (0). The most logical way for this to happen is having an x^3 term which will go away on the fourth derivative.</p>
<p>B is the first one out…each derivative is going to add an x in front of the cos or sin, causing it to always be 0. E is also out because the second derivative will give a term of -2 from the starting -x^2 which will cause the second derivative to have a value that does not equal 0. Next is A which will give a term of -3cosx in the second derivative. C doesn’t work either because the third derivative gives a value of 2cosx, which does not equal 0 either. Therefore, D is left.</p>
<p>Then to check with work, the fourth derivative of D ends up coming out as:
12e^x + 8xe^x + (x^2)e^x, which equals 12 at x=0.
12/4! (to solve for the coefficient) = 1/2 or 1/2!
5th derivative ends up as 20/5! or 1/3!</p>
<p>Do we use pen or pencil on the Free Response section?</p>
<p>It’s math…doesn’t that guarantee pencil…
If it was pen, people would make mistakes and then have to cross out, and considering there is limited space, that would be a huge problem.</p>
<p>Just wondering because i checked the student sample responses on the ap central website and the “pencil” marks sometimes seem thick or bold.
Take a look: <a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;
<p>Pretty sure it is pen because almost all FRQ are pen, but just bring both and they will tell you when you get there.</p>
<p>Since I took the Calculus AB exam and that it has the same testing policy for Calculus BC and I bought my FRQ from last year, you can use “either pencil or pen with black or dark blue ink” (back of my FRQ booklet). However, I used black ink last year.</p>
<p>
I plan to use a mechanical pencil. The 0.5 type lead one so the writing is thin and clear.</p>
<p>hotinpursuit, I’m pretty sure that mechanical pencils aren’t allowed on AP tests…at least, that’s what I was told. Otherwise I’d use the same.</p>
<p>^
Awww I hate that rule. Mechanical pencils are so much clearer and easier to use. On SATs I know they were banned, but APs too…=/
CB’s claim was that people stuff notes inside, but that is so unlikely and useless…
I’m probably going to attempt to sneak it in(over 30 kids in my school are taking BC) and hope that they don’t notice or don’t question it.</p>
<p>sneaking notes into your mechanical pencil. lol Never heard of that before… Anyway, theres not enough time to look at your notes and do the work, you gotta work fast and use every second you have. Trust me, everyones bound to get stuck on at least one problem, skip it and come back. lol i get off topic really easy…</p>
<p>Wait, you guys take all the time to just finish the test? On all the practice tests I’ve done, I’ve had at least 15 minutes to spare for each part of the test…</p>
<p>I am hoping someone can confirm my answer to the following problem:</p>
<p>Limit as x approaches positive infinity of “e raised to the x/x squared”.</p>
<p>(A) 0
(B) 1/2
(C) 1
(D) 2
(E) positive infinity</p>
<p>I believe the correct answer is A = 0. Am I correct on this? TIA!</p>
<p>^Thanks for asking a question.
I would say it is E.
You would first plug in infinity. Seeing as you get infinity/infinity, use L’Hopital’s Rule twice.
That gives you (e^x)/2
Then plug in infinity and you get infinity/2 which is infinity. So E.</p>
<p>Another way you can think of the limit is how fast the numerator “grows” as opposed to the denominator. e^x grows (increases) more quickly than x^2, so as x increases, the value of the fraction gets bigger and bigger until you reach infinity (positive).</p>
<p>Just another way to do infinite limits without L’Hopital’s Rule or a calculator.</p>
<p>speaking of the sneaking in notes and stuff, my teacher told us that you can put anything and everything that fits in your calculator for the test, (as in programs with formulas and stuff) and they won’t mind you using it.</p>
<p>and for that question, cant you say it’s (c)?
because as x>inf of x/x^2 would be x>inf of 1/x (divide numerator and denominator by x) so the lim as x>inf of 1/x is 0. and e^0 is 1 (c)
…or am i mixing this up with series?..@_@</p>
<p>You can use programs in your calculator–which you are allowed to use for only half of the test.</p>
<p>As for the limit, where are you getting the x in the numerator?</p>
<p>isnt that the question?
lim as x>inf of e^(x/x^2)?</p>
<p>Nope
Its badly parenthesed(if thats a word)</p>
<p>the question was lim as x–>inf ((e^x)/(x^2))</p>
<p>If that’s the case, then I would choose positive infinity because of L’Hospital Rule, like hotinpursuit said.</p>