Hi, I'm in AP Calculus and I feel really stupid

In summary, Daniel felt really stupid because he forgot a lot of math over the summer and he was struggling with the review. He posted on a forum similar to ones he's used in the past and asked for help. However, he found out that he was not allowed to use a graphing calculator to solve the first problem. The second problem had two intersections and he was able to solve it using his graphing calculator.
  • #1
Daniel
8
0
Hi, I'm in AP Calculus and I feel really stupid :(

I feel really stupid because it's only the first week of school and I'm struggling with the review (I forgot a lot over the summer)

I'm posed with these two problems (in addition to many other but I don't want to bore you all :)):

(a)Solve for x: x^2 = 2^x
(b)Solve for X: x^2 > 2^x

My first plan of attack for (a) was to do this:

2logx = xlog2

that didn't seem to get me anywhere and now I seem stuck... please help me?

Thanks,

Daniel
 
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  • #2
Also, does anyone know any forums similar to these (not physics though) which can help you with math homework? I posted here because I'm sure a lot of you are in high levels of math too.
 
  • #3
Does re-arranging a) into xx = 22 help you?
 
  • #4
The only real way to do (a) is by inspection. Make a few guesses as to the answer, you'll probably hit upon the two solutions.


As for (b), are you reviewing calculus or previous courses? Are you allowed to solve problems like this by looking at the graph in a calculator?
 
  • #5
I tried graphing too, and that gave me 3 different intersections when I set y=x^2 and y=2^x. I still wouldn't know how to do (b) with graphing, and I'm sure there's a way to do (a) without graphing.
 
  • #6
Originally posted by Daniel
I tried graphing too, and that gave me 3 different intersections when I set y=x^2 and y=2^x. I still wouldn't know how to do (b) with graphing, and I'm sure there's a way to do (a) without graphing.

There is only one intersection for those two lines.
 
  • #7
I found an intersection at 2, -.7666, and one at 4. I used ti83+ and I'm in degree mode.
 
  • #8
As for (b), are you reviewing calculus or previous courses? Are you allowed to solve problems like this by looking at the graph in a calculator?

We are reviewing previous courses. I'm allowed to use a calculator, but I forgot how to with a >.
 
  • #9
Originally posted by Daniel
I found an intersection at 2, -.7666, and one at 4. I used ti83+ and I'm in degree mode.

oops sorry I've mad a mistake.
 
  • #10
just to correct my first post, this is were I made the mistake, i should of gotten:

x1/x = 21/2
 
  • #11
The only way your going to solve this I think is by using your graphing calculator.
 
  • #12
how about part (b)?
 
  • #13
b) should be 2 < x < 4 and x < -0.7666
 
  • #14
basically again just looking at the graph.
 
  • #15
You "solve" inequalities with a graph by seeing which graph is above the other. You determine where each interval ends by "zooming" in on the intersections.

You cannot solve equation like x^2= 2^x (which has x both as a "base" and as an exponent) algebraically (except by using the "Lambert W function" which is specifically defined as the inverse of the function f(x)= xe^x.)
 

What is AP Calculus?

AP Calculus is an advanced placement high school course that covers the fundamentals of calculus, including limits, derivatives, and integrals. It is typically taken by students who have completed pre-calculus and are interested in pursuing a college degree in a STEM field.

Why do I feel stupid in AP Calculus?

Feeling overwhelmed or confused in AP Calculus is not uncommon, as it is a challenging subject that requires a strong foundation in algebra and geometry. Additionally, the fast-paced nature of the course can make it difficult to keep up with new concepts. However, with dedication and hard work, you can overcome these feelings and succeed in the class.

What can I do to improve in AP Calculus?

To improve in AP Calculus, it is important to actively engage in class and ask questions when you don't understand something. You can also seek extra help from your teacher or a tutor, review class material regularly, and practice solving problems on your own. Additionally, staying organized and managing your time effectively can also contribute to your success in the course.

Is AP Calculus worth taking?

While AP Calculus may be challenging, it is a valuable course for students who are interested in pursuing a career in a STEM field. It not only provides a strong foundation in calculus, but it also demonstrates to colleges that you are capable of handling rigorous coursework. Additionally, earning a high score on the AP Calculus exam can potentially earn you college credit, saving you time and money in the long run.

How can I prepare for the AP Calculus exam?

To prepare for the AP Calculus exam, it is important to review class material regularly, practice solving problems from previous exams, and take advantage of review materials provided by your teacher or online. It is also helpful to familiarize yourself with the exam format and timing, as well as strategies for approaching different types of questions. Lastly, make sure to get plenty of rest and eat well before the exam to ensure you are mentally prepared on test day.

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