Welcome 2016-17 BC Calculus Students! You should have been given a
summer work packet to prepare you for our journey into the study of
calculus this fall. If you have not received your packet, or want
another copy, you can download it from the website.
Past students have found this review to be very helpful upon
undertaking the study of calculus, and I'm sure you will, too!
Use this forum to post questions and discuss solutions regarding the
summer packet. Look to offer help to those who ask and post your
questions when you have them. There is only one rule on this forum:
ALWAYS RESPECT EACH OTHER! You can also refer to the discussions from previous summer work packets - just scroll down.
Some reminders:
1. the packet is due the first day of class for
a significant grade
2. your original work should be on separate paper
and done without a calculator except when specified
3. there are helpful links on the course website (you should familiarize yourself with our website!)
**Follow on Twitter: @GrovesBCcalc**
Good luck! See you in September! ~Coach Wilson
Hi Coach Wilson!
ReplyDeleteFor Week 1 are radicals alright to use in the exponents section when fractional exponents have been otherwise simplified as far as they can be, or have I messed up somewhere and all the exponents work out to positive integers without needing a radical to clean things up?
Also, for Week 1 problem 9 I can get the domain, start of the range, the value that the function approaches as it goes off to infinity, but I'm unable to find the maximum value of the range. Are we supposed to use the domain of the inverse, a table of values to give an estimate of the maximum, or some other method in order to find the maximum?
You may leave your answers with simplified fraction exponents, which we will find are much easier to work with than radicals.
ReplyDeleteFor 9, the numerator provides a half open domain, so consider what the output of the function is at the closed endpoint and then as x approaches infinity.
Hope this helps.
Just for clarification, Week 2 Question 11 has a degree symbol in it. This denotes multiplication, right?
ReplyDeleteThat is the composition of the function h onto f.
DeleteFor the second System equation in Week 2 are we supposed to find what values of x make the absolute value of x equal to the quadratic? I just wanted to clarify since there were no equal signs in the problem itself and I was a bit confused.
ReplyDeleteYou are correct. Use the hint provided and make two separate equations.
DeleteFor Week 2 Question 16 it says to calculate the logarithmic expression by hand, but uses numbers that do not come out cleanly by hand. Should we just simplify it as best we can? Thanks!
ReplyDeleteP.S. I have a feeling that the problem may have been intended to have the base of the log be 3, instead of 4, because that makes the solution a lot prettier. Or it could be that I'm just missing something.
If it does not simplify to an exact value, you may leave the expression in the form log X of the given base.
DeleteFor Week 3 Question 26, I found the values of a-d, but I'm not sure how to answer if the leaf is moving up/down or changing directions. I am guessing that if the answer is 0 the leaf is changing directions and if it's positive it's moving up?
ReplyDeleteThis question also applies to Question 27, because I'm not really sure what it's asking. I'm pretty sure the weight moves most rapidly in the middle the the oscillation, but I don't get how to find the x values.
I suggest graphing the functions. There is only one X value each for 27 due to the damping function.
ReplyDeleteEXTRA CREDIT OPPORTUNITY: Most students sign up for calculus but have no idea what it really is or why it's an important branch of mathematics. Look at the links below and watch the 7 minute video regarding who invented calculus. Then, write 2-3 paragraphs that answer all of the questions below. Turn this in on the first day along with your summer work for extra credit (please staple this page on the top). This will be the homework for day one of class anyway, so you might as well do it early and get some EC!
ReplyDeleteLinks:
http://www.mathscoop.com/calculus/what-is-calculus.php
https://www.mathsisfun.com/calculus/introduction.html
https://www.youtube.com/watch?v=axZTv5YJssA&autoplay=1&app=desktop
Questions to answer:
1. Summarize what calculus is
2. Describe something(s) you hope to learn/gain from this course now that you have a bit of an idea what we will learn about
3. Why are you taking this course? (don't answer "because it follows honors pre-calc", give some thought here)
4. Convince me who invented calculus (pick one and argue your position)
Feel free to cite sources other than those I provided!
See you next week!
Coach Wilson
My apologies that the links are not "clickable" (did I just invent a word?). Please copy and paste them into your browser.
Delete1. Summarize what calculus is
DeleteCalculus is the study of change and accumulation in math. Algenra gave us the tools to be able to evaluate sloped of simple linear equations, but calculus allows you to be able find the slopes of curves as well. This is diferencial calculus, howver, integrl calculus allows you to find the area beneath the curves. This understanding of fundamental mathmatics is critical for our knowledge of physics and the real world.
2. Describe something(s) you hope to learn/gain from this course now that you have a bit of an idea what we will learn about
I hope that this course will help strengthen the physics that I have already taken. I realize that we will be evaluating velocity vs. time graphs, and I must be able to use calculus in order to calculate the slope of the curves, as well as the total distance traveled (area).
3. Why are you taking this course? (don't answer "because it follows honors pre-calc", give some thought here)
I am taking this course because I felt that math was one of the subjects I needed to challenge myself in headed into college. I feel that if I do not subject myself to advanced calculus, then i would struggle in my college courses, and indeed my career in general. Calculus is an essential building block for my future education.
4. Convince me who invented calculus (pick one and argue your position)
Feel free to cite sources other than those I provided!
Isaac Newton, the grandfather of modern physics, invented calculus in order to further explore the exciting world of physics. He worked with fluxionary calculus, exploring rates of change. Ultimately, we owe two of our subjects in school to him.
-NATE WAGNER
Hi Coach,
ReplyDeleteFor clarification, on Week 3, Question 23 are we just looking for the range of the function? Also, do you recommend changing the equation to be all sine or cosine?
23 should be =0, not h(x). Typo...I suggest using an identity for the half angle cos(x/2). Or, you can use a double angle identity for sin x since x is double x/2
DeleteHey y'all! How do you recommend going about solving w4q21? I did the theorem and got something along the lines of sinxcosh + cosxsinh - sinx. What do we do from there? Is there something I'm blatantly missing? Thanks!
ReplyDeleteNow take the limit as h approaches zero.
DeleteHey for the matching, there are more equations than graphs. Is this intentional? Do we just scratch it out if there is no matching graph? Also, how do we tell the difference between y = ln x and y = log x? Aren't they basically the same?
ReplyDeleteThere are more functions than graphs, yes. To your second question, consider the inverses e^x and 10^x. You should immediately see how these graphs vary.
Deletebut in the context of the graphs. I didn't count the individual lines, but it seems difficult to tell. One of the graphs is obviously something^x, but the graph is too small to tell whether it is 10 or 2
DeleteIn w1q37, what does it mean "remove the discontinuity"? What do I do?
ReplyDeleteFill the hole by defining the function at that point.
Deletefor week 2 under the systems section, #2 has no equal signs. What do we do?
ReplyDeleteNever mind you answered that earlier above. My bad.
DeleteRegarding Week 2 Question 11 under logs and exponents, can we assume the bacteria starts with one cell?
ReplyDeleteYes
Delete