My Happy Ever After(discontinued)

6:It Was Him? Why?

hi its boringly friday why you ask well somebodys been pullaaahhhhh..... see what i mean i fell because of butter prank as i was saying somebodys pulling of tricks on me and the bad part is i dont know who he/she is and the worse part hes not stopping and the worse worse part i dont know the reason why? *inhales exhales* what am i going to do i cant sleep because of thinking who it might be and its affecting my studies last time my prof ask me what is the difference between algebra and calculus? well good thing i know that then i answered Algebra II deals with learning factoring, completing the square, solving quadratic equations. Basically, in Algebra we teach you how to do every possible thing to a seconok d degree polynomial (a quadratic). you also learn of conic sections. You will only see a cubic if it has x = 0 as a root with a remaining quadratic as a factor. or sometimes, when learning the rational root test you will have a higher degree polynomial. In algebra II you also learn of e and natural logarithms, and logarithms.

In Calculus you will apply all of those techniques. However, Calculus is much more advanced than simple algebra. Calculus deals with instantaneous rates of change. It deals with the infinite. It deals with dividing something into infinitely small pieces.

to give you an idea of how calculus differs from algebra, an example would be the parabolic shape (due to earth's gravitational pull) of a foot ball thrown from a quarterback.

in algebra, you will have learned that this, as a position function f(x) with respect to time x would be something like:

f(x) = -16x^2 + 10x + 5

from skills in algebra, you should be able to tell the vertex of the parabola will be the maximum height.

in calculus, you learn that the parabolic shape that is formed is from the acceleration of earth's gravitational pull and will be able to calculate the instantaneous velocity of this projectile in motion.

the height (at the vertex) would also be given by the tangent line of the function when it = 0. (no slope)

imagine this, a train runs off of a curved track at some point, and from the inertia of the train it travels at a 'tangent' to the track at that given point. those tangent lines are what you will learn in the first semester of calculus (this is the intantaneous rate of change).

the idea of the first semester of calculus is the idea of tangent lines.

from the slope formula of a line you have:

the slope through (x1, y1) and (x2, y2)

will be :

(y2 - y1) / (x2 - x1)

imagine that the points become infinitely close (indeed they would be come the same point)

so consider the second point to be (x + e, f(x + e)) (x + e is some length e more than x)

the slope between the two points, (x, f(x)), and (x + e, f(x + e)) with the formula gives:

(f(x + e) - f(x)) / ((x + e) - x)

=

(f(x + e) - f(x)) / e

as these points become infinitely close (e goes to zero)

we have the tangent line of the function at that point.

a tangent line is given from the 'derivative' of a function.

also, imagine approximating the area of an oil spill. if you were to divide the area into chunks with a known length of each side of the chunks, you would get a closer approximation for the area of the oil spill as those chunks get smaller and smaller. and you get the true area of the oil spill if you divide the area into infinitely small chunks. This is what you will learn in the second semester of calculus.

in second semester of calclus you learn about 'anti-derivatives' aka 'integrals'

Calculus deals with the infinite. students who have a hard time in calculus lack algebra skills. But if you have a good foundation in algebra, you should be fine in calculus.

Calculus is the greatest scientific accomplishment to this date, by the way. It is also what spawned the age of enlightenment and scientific revolution. so yeah see im smart but the other questions i cant answer wow the validictorian forever cannot answer simpl questions

wait i saw carl preparing pranks what it was him why
A/N sorry guys yun suddenly sa chapter seven para may flashback and sorry sa slowly update grounded kasi eh balaw ang gadget good thing i found my cp hahaha so yeah wait for the next update