Fun Post: Getting kicked in the nuts

Ladies, I understand that you have it hard, but don't think we don't have it hard either. Our sensitive area that contains our babies are extremely precious. There is no greater physical pain than having this space violated.
Here's a video that has both math and nut shots in it. I know you want to see it. Btw, this guy is like a beast.
https://www.youtube.com/watch?v=pB7gnB31NnI
https://www.youtube.com/watch?v=a86cQobU-n4

Introduction to limits

Definition of limit:

If f(x) becomes close to a number L as x approaches c from either side, the limit of f(x) as x approaches c is L.

Lim.  F(x) = L

X->c

Another way to define a limit is a point where an approaching line or graph ceases to pass.

How do numerically estimate a limit 

As seen through this example, we simply substitute values extremely close to c into f(x). After finding these various results, we should be able to estimate the value that resembles the limit. 

Through graphs we can tell if the function has a limit or not.

No limit: lines will never intersect. (|x|/x)

1. F(x) approaches a different number from the right side of c

2. F(x) increases or decreases without bound as x approaches c

3. F(x) oscillates between two fixed values as x approaches c.

Limit: lines intersect

Professions that use math

What's up mathland!?
As a fellow high schooler, I also wonder what is the relevance of using math for the future. Doesn't calculus seem a little bit pointless for many professional occupations? That is why Im giving a list of professional jobs using math.

The main sections of jobs that use math are...
income - economists, bankers
future outlook - statistics, actuaries, researcher.
physical demands - physicians,
job security
stress
work environment.

In general, we may need to know more math math skill than we think we do. Therefore, we should take math more serriously than we should believe it or not.

11.2-vectors In space

R,emeber that a vector is a line with direction and magnitude. It is denoted by v=<v1,v2,v3>

To find the points of a vector we usually subtract the terminal point by the initial points

Here a few things regarding vectors in space

Let's say we had to give the component form, the length, and unit vector of v with initial point (3,4,2) and terminal point (3,6,4).

V= <3-3,6-4,4-2> = <0,2,2> 

||v|| = [2^2+2^2]^1/2 = 8^1/2

U = <0,2,2>/8^1/2 = <0,1/2^1/2, 1/2^1/2>

Angle between two vectors 

Cos theta = (u * v)/||u||||v||

11.1-the three dimensional coordinate system

X= distance from yz-plane to P

Y=distance from xz-plane to P

Z=distance from xy-plane to P

Distant formula

D=[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]^1/2

Let's say we had to find the distance between (2,1,3) and (-1,2,1)

D= [(-1 - 2)^2 + (2 - 1)^2 + (1 - 3)^2]^1/2

  = [ 9 + 1 + 4]^1/2

  = (14)^1/2

Midpoint 

((X1 + x2))/2, ((y1 + y2))/2, ((z1 + z2))/2

Let's say we had to find the midpoint between (5,-2,3) and (0,4,4)

(5+0)/2, (-2+4)/2, (3+4)/2) = (5/2,1,7/2)

Standard equation of a sphere

[(x-h)^2 + (y-k)^2 + (z-j)^2] = r^2

Cool 3d graphs

Z=-1/(x^2+y^2)

Z = cos (abs x + abs y) * (abs x + abs y)

Z = -x*y*e^(x^2-y^2)