Beach - Sandy Andy

a) R(t) is the rate at which sand is being removed by cubic yards/hour, so if you take the integral, it would give you the amount of sands by cubic yards (which the question is asking for )
eq: fnInt (2+5sin((4 pi t)/25), x, 0, 6) = about 31.816, so at t = 6, 31.816 cubic yards of sand has been removed

b) asking for amount of sand, so integral is needed,
fnInt(S(t)), x , 0, 6) - fnInt (R(t)), x, 0, 6) + 2500

c) asking for the rate, so no need to integrate, just plug in t=4
so... S(4) - R(4) = -1.909,
so at t = 4, the amount of sand is decreasing by 1.909 cubic yards/hour

d) Asking for amount of sand, so the graph of S(t) - R(t) would give you the slope, when the slope changes from - to +, you'll have a min,
at t= 5.1179 you have a minimum, that is where slope changes from - to + on the graph of S(t) - R(t) (slope graph)

Mean Value Thm

1. Green line - secant, blue-tangent

slope of point c is equal to f(b)-f(a)/b-a

2.Discontinuity and not differentiable functions prevent the slope of the tanget line and secant line from being parrallel

f(x) vs f ' (x)

1. From the Interval (-2,0)U(0,2), f(x) is increasing, f ' (x) is the slope of f(x), and the in that interval, the points are positive, positive slope = increasing
From (-infinity, -2) U (2, infinity), f(x) is decreasing, because the slope is negative, points on f ' (x) graph are negative in that interval

2.At x= -2, f ' (x) changes from negative to positive, making it a local minimum.
at x = 2, f ' (x) changes from positive to negative, making it a local maximum

3. In the interval (-infinity, -1.5) U (0,1.5) , the slope of the f ' (x) graph is positive, f ''(x) > 0 is concave up
in the interval (-1.5 , 0) U (1.5 , infinity), the slope of f '(x) is decreasing, f ''(x) < 0 is concave down

Which Mindset am i?

1. I think i am most likely in the Growth Mind-Set group because..

• Take on challenges
• Move my way over obstacles and..
• see effort as a way to master

2.By taking this class, i knew before hand that it was going to be a challenge, also i've worked my way over my problems in this class, and the effort paid off.

3.Its interesting, because now i know that i could really become more intelligent if i tried.

4.It'll really get me to take on more challenges, and do the same thing i've done in this class, and see how much more intelligent i'll become.

Algebra Vs. Calculus

1. The difference between f(c) and f(x) x->c ...
When your finding the limit as x approaches c, your output is getting closer and closer to that constant, but when you plug in c, you automatically get an output.

2.Simmilarities between slope of a line, and derivative...
To find the slope of a line, you need the change of y/x, and to find the derivative, the first step is finding the slope, so they somewhat need each other.

Limits?

I understand limits, for the most part
these are some problems I'm still not sure about

1) lim 3 sin4x/sin3x
x->0

2) lim sinx/2x^2-x
x->0

3)lim sin^2x/x
x->0

Would appreciate help, thanks

Colleges!

1. a)Music Performance-
To major in music performance, i learned that i need to put a lot of time and effort into it. Spending weeks to learn songs and performances. Also being self-disciplined and able to take criticism well. Taking music classes in highschool is a definite advantange.

b)Music Theory and Composotion-
This major is mostly about learning how to see, read, and right music down by listening to it, or making it up. Takes long hours rehearsing and playing your instrument, and the ability to learn how songs can please your ears. Taking a music class in highschool helps for this major as well. I've always wanted to work with computers.

c) Computer Engineering-
This major is mostly about learning how computers work, just like knowing how a car works. Also, gives you the ability on how to make computers smarter, faster, and more efficent. Taking Calculus, chemistry, and computer classes could be very helpful

2.a)CSUN..also California Institute of the Arts
offers Music Performance as a major, so i find that cool since thats one of the schools i was planning to attend.

b)Both CSUN and California Institute of the Arts offer Music Theory and composition. Same reason why i find it interesting.

c)CSUN, and California Institute of Technology are the only University's that really got my attention, UCLA and USC are the schools most kids want to go to, i'd rather go else where. CSUN same reason, Cal Institute of Tech seems like a school that focuses on technology, so thats basically why i choose that.