The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by

A pumping station adds sand to the beach at a rate modeled by the function S, given by

Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for . At time t=0, the beach contains 2500 cubic yards of sand.

(a) How much sand will the tide remove from the beach during this 6-hour period? Indicate units of measure.

First plug integrate the function at with the x values fnInt(2+5sin(4pi t/25),x,0,6)

shoul get =31.816^3 yds

(b) Write an espression for Y(t), total number of cubic yards of sand on the beach at time t.

y(t)= fnInt(s(t)-fnIntR(t)) dt +2500

(c) Find the rate at which the total amount of sand on the beach is changing at time t=4.

y'(4)= { (15t/1+3t) dt - { (2+5sin(4pi t/25 dt + 2500

=

plug in 4 and integrate result=-1.908 yd/hr

(d) For

, at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.

find where the y1-y2 gives you 0 or undefined. (critical points)

at that x value plug in to the funvtion integrate and final result will give you the minimum value.

The function f(x) from the graph f '(x)

1. f(x) is increasing at the intervals (-2,0)U(2,0)


f(x) is decreasing at the intervals (-infinti, -2)U(2, infinti)

where f '(x)>0 f is increasing & f '(x)<0function is decreasing


2. at x= +/- 1.25 local max. the slope increases then decreases so they have to be max's.


3.concave up at (-infinti, 2) concave down (2, infinti)

we know where f is increasing up and then decreasing down determining the concavities.


4.quadratic maybe end behavior of x to the power of 5.

My Mindset?

1. When it comes to intelligence i understand yes i am who i am but i too know it deosnt end there i understand that my intelligence can change. the same a baby into a teen and a teen into an adult. I belive it just takes some time and patience for example the more stress you apply to a muscle yeah it hurts but it becomes stronger. another example would be ways of life you may not live a certain lifestyle but as you apply it into yours you get stronger, lifestyle wise of course. According to the reading i hope i am growth mindset and if others see me as fixed then i can also change my mentality.

2. This has hurt me in math due to the fact that i fully understand that my intelligence can change and i could learn more... this means more work. however more work means that eventually the subject should get easier. i just have to pace myself and try to stay onboard during whatever climate. Help from the captain and the instructions last but not least my fellow crew.

3. When i read the news i immedialtey thought of a fighting style example muay thai and the muscles you train. first the start off normal then you build and develop better skill.

4.The future looks brighter, iHope on. i just cant stop here there is more to accomplish.

Algebra vs Calculus

Finding the limit of a constant and the output of a constant.

• Fnding the limit of f(x) as x->c could have two different ouputs.

For exapmle: the function f(x)=x/absolute value x the limits as x->0+ side equals 1.

and as the limit as x->0- equals -1. however

• Plugging in the constant will only give you one output.

When just plugging the number 0 it gives you only one output. In this case however there is no output for f(0).

• These two cases could be the same when the limit as x approaches the constant and when just plugging in the constant are equal.

For example: the function f(x)= x^2

The limit as any constant from both the positive side will give you one output.this goes with plugging in the constant too because it gives you the same output.

basically: limit x->c+ f(x)=limit x->c- f(x)=f(c)

Difference between slope of the line and the derivitave.

• The slope of the line.

The slope of line only determines the slope for that single point.

• Derivitave

The derivitave gives you the formula to find the slope for function to every direction of the function so the function must be continuous.

• They are similiar because the give the dx/dy for the given point.

i have reached my limit...

what i dont get about limits

-one thing i don't get about limits is when to plug it it. because occasionally you have to solve first then you can plug it in. what makes it right to solve first then plug it in until it cannot simplify any longer???

ex: lim 1/2+x-1/2/x

x-->

to solve first you ave to find the least common demonator for the fractioned numerator but why cant you just

what i do get.

2. the limit of a constant will always give you that constant as the answer.

3. you can occasionally brake limits apart. that can make it easier because you ccan then find the limit for the separate equations.

COLLEGE and MAJORS

3 Majors:

1.Computer science- majors learn about computer systems and the way humans and computers interact from a scientific perspective. Instruction includes the theory and design of hardware and software.

2.Computer engineering- majors learn to analyze, design, and develop computer hardware and software.

3. Civil engineering- majors learn how to use math and science to design big construction projects. Topics covered include the calculation of how much weight a structure will hold and the environmental issues that surround construction.

3 Colleges:

1. UCLA.

admitted 23% applicants accepted not easy but possible.

2. POLY POMONA.

admitted 53% applicants accepted not an easy chance but possible.

3. UC BERKELEY.

admitted 22% applicants accepted very not easy but possible as well.

?TIPS AND HINTS?

1.Transformation?

first thing that comes to my mind when i hear transformation, same graph just sabotaged. this helps you know that the x is still itself and whatever is being added or subtracted to the input means it either shifts to the left or right about the x-axis. + to the left - to the right. and then more sabotaging...when the output is either added or subtracted to the graph moves either up or down about the y-axis. + up - down.

2. trigonometry?

hmmm...first relate trigonometry to every type of math you have taken in your life smashed together in some sort of frenzy. basically the relations between sides and angles not only using geometry but algebra as well. estimations , add, subtract, multiply, divide, you name it. it will be found in trig. as long you get those bases down you be fine and apply them to solve for every type of arithmetic.

3. what confuses me?!

what can i start with okay everything confuses me. one topic which we have been working on i am having difficulties to fully understand. inverses! logs! they seem to make sense but i still forget how to separate them when they can be and when its a function and when it is not a function.