FR 5

A)R(t)=rate of which sand is removed. The is how much is being removed. so take the integral. So to see how much the tide take away the first 6 hrs set the integral from 0-6 making the equation:
fnInt(2+5sin(4nt/25),T,0,6) = 31.81593137 simplified it is 31.816 cubic yards

B)To fond the amount of sand at a certain time you must subtract S(t)-R(t)since there is no exact time but a starting point the integral will be from 0-x. At t=0 there is already 2500 sand so it must be added so the equation is:
Y(t)=2500+fnInt (S(t)-R(t), t, 0, x)

C)Y(t)=total number of cubic yards of sand on the beach. Y'(t)=rate at which the total number of sand is changing. so the derivative is Y'(t) is just S(t)-R(t). now we just have to find it at t=4 giving the equation Y'(4) = 15(4)/1+3(4) - 2 + 5sin(4(4)π/25). After the simplifying it equals Y'(4) ≈ -1.909 cubic yards/hour.

D)To find the minimum amount at the equation at part A don't you graph it and find the intersection. If so then the intersection is at (5.1178, 4.6943)so at 5.1178 it equals 4.6943 + 2500=2504.6943 cubic yards.

DONE???

MEANIE

The mean value theorum means: F'(c) is the derivative at x=c and the slope of the secant line through the interval [a,b] is F(b)-F(a)/b-a all this basically means this Point of Secant line is equal to the Point of the Tangent line.
For Instance my graph would be x²


lets say the intervals are from [o,3] so then a=0 and b=3 now we got the points now all we need is to use them in the equation and find c so F(3)-F(0)/3-0 =3 so the slope of the secant line is 3 and the equation is the derivative 2x



Ok so skipping all of the equations blah blah blah we find that c lies on x=1 and knowing that we can do the tangent line. Which again blah blah blah we find that it passes through (1,1)and since the tangent line is parallel to the secant use that knowledge and pont slope form and then we get the equation F(x)=2x-1 and bam definition graphically



2. this doesnt work for equations that end up being cusps, corners, etc like and absolute value equation it is not diferrentible at x=0 so there is no tangent point there right? hehehe

F(x) to F'(x)

1) It increases at (-2,0)U(0,2) because durint those intervals it only output positive numbers basically f'(x)>0. It decreases at (-00, -2)U(2, 00) because f'(x)<0

2)at (0, 0) Right? Because an extrema is when F'(x) is zero or undefined

3)Concave up:(-00,-1.5)U(1.5, 00)
Concave down: (-1.5, 1.5)
concave up wher the slope is positive and concave down wher it is negative

4)it is probably x^5 cause it changes direction a couple of times also because the f'(x) looks like x^4.

Mind Boggling

1. I am a growth mindset I always like to learn new things. i belive that anybody can improve themselves.
2. It helped me because it allowed me to stick to math because I love challenges.
3. Makes me want to exercise the hell out of it i could make better than ever before. Funny because even though I am not in shape my brain could be.
4. It allows me to know that I can push myself a lot further than I know.

Algebra VS Calculus the BIG fight

1) Finding the limit at x=c of a function is actually finding the value as x approaches the constant (c) which turns out to be the y value. Now f(c) is looking for the output when x is c I think that's what I'm trying to say. The output doesn't have to be the same as the limit of x=c but if the limit at x=c is the same as f(c) then the function is continuous and it is only continuous when it is like this. Right?...

2) Both the slope and derivative use the change in y/ the change in x formula but for the slope their is no lim unlike the derivitive where the lim is when h->0 so the difference in the equation would be lim h->0 f(2+h)-f(2)/h where h is how many point away from the initial point. Also a slope would the slope (obviously) of a specific line where a derivative would be involved with Tangent lines of curves.

This is what I got probably very arguable but eh screw it I tried...

What's my limit?

1) I always try to avoid any problem involving Sin(x)/x I do not know what exactly to do I get confused to where am I supossed to plug in the limit especially when it is zero

2) The other types of problems that I have trouble with are the problems with fractions in fractions. For instance, [(1/x+1)+(1/2x)]/x these types of problems get me stumble because I forget how to simplify the problem. Then the same thing about plugging in the limit especially when it is zero...damn zeroes.

3) Int type problems just stumble me. I know how they look but I can't graph them without using the calculator and I really do not know how to find the limit at all I try but fail HELP!!!

Toga College Party WOOOOOH

1) -General Engineering- Associate’s degree level provides solid preparation for any type of engineering degree at the bachelor’s level and if one continues to get their degree in this field they get more education on different type of engineering and business. Also use your invention in a field that has nothing to do with engineering.

-Psychology- Well modern psychologist do what the ancient Greeks do in which they study the mind by asking it questions (not literally...well kind of) asking these questions one learns why one acts a certain way, how one can deal with their struggles that placed in front of them, etc. A whole lot of "I'm in your mind" type stuff.

-Music Performance- As "kick back" of a class as one can get but that's not the reason I want it. This major allows one to practice their music to allow skill to develop. Also in this process one will have to come up with their own sound that signifies them.

2) -MIT- Best Math school, including Engineering, there is. Have been banned from certain competition due to the fact that they keep winning them. Also it is a private 4 year that only 12% of people get in who want to get in. They offer a Bachelor's, Master's, and Doctoral

-University of California: Berkeley- Public 4 year university that offers Bachelor's, Master's, Doctoral, and First Professional. 22% of people who apply get in.

-University of the Arts- This is a private 4 year university.Offer Bachelor's and Master's degree. Only 8% of their students who got in had a 3.75 GPA in HS...Wow I thought it would be higher woohoo i can probably get in.

Note: Going to college seems challenging but oh well time to step it up I guess