June 23, 20XX
Jolting down, touring, and seeing more memorabilia and advertisements on the eastern side's walls with lots of key sentences and quotes:
"Dr. Mario teaching the class how medical anatomy is similar to block dropping with strategic thinkings"
"A village inhabited by anthropomorphic animals"
"Mobile Golf provides an enjoyable and portable golfing experience for players on the go!"
"Players can choose from a selection of racing tracks, utilize power-ups to gain advantages, and compete against computer-controlled opponents or friends through multiplayer options!"
"Luigi, Mario's brother, as he explores a haunted mansion in search of Mario, who has gone missing. Armed with a ghost-catching vacuum cleaner"
"Mario, Link, Pikachu, and many others engage in battles against notorious villains"
"Daily activities such as fishing, bug catching, fossil hunting, gardening, and interacting with the animal villagers"
"Mario or Luigi as they traverse various colorful and challenging levels, defeat enemies, and rescue Princess Peach from the villainous Bowser"
"Mario embarks on a tropical vacation to Isle Delfino, where he finds himself embroiled in a mission to clean up the island and clear his name while being framed by Bowser Jr's Shadow Mario. Equipped with a water-spraying device called FLUDD, Mario must navigate through vibrant levels, solve puzzles, and battle enemies"
"This game features unique artistic visuals, inventive level design, and gameplay mechanics that involve flutter jumping, egg-throwing, and a charming and whimsical platforming experience!"
"The objective is to collect the most stars and coins to emerge as the victor with a gaming experience, encouraging friendly competition and cooperation among players!"
"Players can enjoy various mini-games with different themes each offering its unique challenges and objectives!"
"Players can choose their favorite puzzle game and challenge themselves to solve puzzles and clear levels!"
"Wario and his video game company, WarioWare, Inc taking over multiple blocks"
"More fishing, bug catching, fossil hunting, and interacting with the villagers"
"Mario or Luigi as they embark on another quest to rescue Princess Peach from the clutches of the villainous Bowser"
"Mario, Luigi, Peach, and Bowser, and compete in golf tournaments across colorful and imaginative courses and doing competitive golfing with friends"
"Themed race tracks filled with power-ups, obstacles, and shortcuts. Players can engage in single-player races, battle modes, or compete against friends in multiplayer races"
"Players engage in a variety of mini-games that test their skills and luck!"
"Mario and Luigi as they journey to the Beanbean Kingdom to retrieve Princess Peach's voice, which has been stolen by the evil witch Cackletta and her minion, Fawful"
"This game features a cooperative competitive gameplay dynamic, encourages strategic play and communication between players, and resulting in engaging and intense multiplayer matches!"
"This game retains the simple yet challenging gameplay of the original, allowing players to experience the timeless classic on a handheld console!"
"This game features side-scrolling platforming levels, power-ups, hidden secrets, and memorable enemies!"
"This game features RPG-like elements, such as leveling up characters, upgrading equipment, and unlocking new courses!"
"Dr. Mario helps anonymous patients who are extreme addicts"
"Mario and Luigi as they work together to defeat enemies by knocking them over and then kicking them off"
"Mario as a demolition worker tasked with destroying objects"
"Mario as he tries to rescue a group of toys packages that have been stolen"
"Mario's quest to rescue Princess Peach and uncover the secrets of the mysterious Thousand-Year Door"
"Mario and Luigi as they navigate through Mushroom Kingdom, facing off against classic enemies and overcoming difficult platforming sections"
"This game combines traditional pinball gameplay with elements of platforming and puzzle-solving, creating a unique and enjoyable pinball experience!"
"This game features a series of mini-games with different objectives and challenges, ranging from racing to platforming to puzzle-solving!"
"This tennis game has fast-paced tennis gameplay!"
"This party game offers a lively party experience with various mini-games and board game elements!"
"This game has the handheld console with enhanced features and additional playable characters"
"Players navigate levels by manipulating gravity"
"Portable party game featuring a unique single-player-focused campaign with various mini-games to enjoy on the go"
"Sonic rescuing flicky birds from the clutches of Dr. Robotnik"
"Sonic and his friends embark on an adventure to stop the villainous Chaos from destroying Station Square and save a mysterious creature named Tikal and the Chaos Emeralds"
"Sonic (with the help of Mario and Luigi), alongside his friends and new confrontations, Shadow and Rouge, races against time to stop the plans of Dr. Eggman and the military organization G.U.N while discovering the truth about their own origins"
"Sonic, Tails, and Knuckles team up with other characters to form Team Sonic, Team Dark, Team Rose, and Team Chaotix, as they race against Metal Sonic and Dr. Eggman to save the world from their nefarious schemes"
"Shadow, plagued by amnesia, embarks on a quest to uncover his past, facing choices that determine his path as he battles against multiple factions and attempts to prevent a planetary disaster caused by the invasion of the Black Arms"
Math Notes: (filled with academic musings)
L'Hosptial Rules:
1/infinity = infinity
0/1 = 0
lim x to 0: 3sin(4x) / 5x
lim x to 0: 3sin(4(0)) / 5(0)
lim x to 0: 3sin(0) / 5(0)
=0/0
Using Chain Rule: f(x)=f(g(x))
f '(x): 3cos(4x)(4) / 5
lim x to 0: 3cos(4)(0)(4) / 5
3 cos (0)(4)
3(1)(4)/5
=12/5
lim x to infinity: 4x^3 - 2x^2 + 6 / Pi x^3 + 4
f '(x) = lim x to infinity 12x^2 - 4x / 3 Pi x^2
f "(x) = lim x to infinity 24x - 4 / 6 Pi x
f "'(x)= lim x to infinity 24 / 6 Pi
=4/Pi
Integral -4sin(4x)dx
u=4x
dy/dx = 4 (dy/dx)
du=4dx
dx=du/4
Integral -4sin(u)(du/4)
Integral -sin(u)du
=cos(u)+c
=cos(4x)+c
Integral (3x^-2 - 4x^2 + 1)dx
Anti Derivatives Involved
Integral (3x^-2 - 4x^2 + 1)dx
Integral 3x^-2 dx - Integral 4x^2 dx + Integral dx
=3x^-1 / -1 - 4x^3 / 3 + x + c
=-3/x - 4x^3 / 3 + x + c
Integration Using the Power Rule
Integral (x^4 - 3x^3 + 5x^2)dx
Integral x^n dx = x^n+1 / n+1 + c, n should not equal to 1
Integral x^-1 dx = ln |x| + c
x^5 / 5 - 3 (x^4 / 4) + 5 (x^3 / 3) + c
1/5 (x^3 - 3/4 (x^4) + 5/3 (x^3) + c)
Exponential Function
Integral e^u = e^u
Integral 9e^12-3t dt
Integral 9e^12-3t dt = 9e^12-3t/12-3t + c
Integral e^u du = e^u + c
u=12-3t
du/dt = -3
dt=du/-3
Integral 9e^u (du/-3)
=9/3 Integral e^u du
= -3e^12-3t + c
Integral e^4x dx = e^4x / 4 + c
e^4x / 4 + c
Integral e^5x dx = e^5x / 5 + c
Integral e^x dx = e^x / 1 + c
Integral 8e^2x dx = 8e^2x / 2 + c
=4e^2x + c
Integral 12e^3x dx = 12e^3x / 3 + c
=4e^3x + c
Trig Functions
Integral cos (x) dx = sin x + c
Integral sin (x) dx = -cos x + c
Integral cos (3x) dx = sin(3x) / 3 + c
Integral cos (7x) dx = sin(7x) / 7 + c
Integral 14 sin (2x) dx = 14 (-cos 2x) / 2 + c
= -7cos(2x) + c
Trig Functions
Integral 6sin (3x) dx
= 6 (-cos 3x) / 3 + c
= -2cos (3x) + c
Integral sec^2 (x) dx
=tan x + c
Integral 8 sec^2 (4x) dx = 8 tan (4x) / 4 + c
= 2tan(4x) + c
Integral sec(x) tan(x) dx
= sec(x) + c
Integral 12 sec(3x) tan(3x) dx
=12sec(3x) / 3 + c
= 4 sec(3x) + c
Integral x^2 sin(x^3) dx
u=x^3
du=3x^2 dx
du / 3x^2 = dx
Integral x^2 sin (u) du/3x^2
1/3 Integral sin(u) du = -1/3 cos(u) + c
-1/3 cos(x^3) + c
Integral 5x [x^2 + 3]^4 dx
u=x^2 + 3
du=2xdx
du/2x = dx
Integral 5x [u]^4 du/2x
5/2 Integral u^4 du = 5/2 u^5 / 5 + c
=1/2 u^5 + c
=1/2 [x^2 + 3]^5 + c
Integral tan x dx
u=cos x
du= -sin x dx
Integral sin x / cos x dx
du= -sin x = dx
Integral sin x / u (du / -sin x)
-Integral 1/u = -ln |u| + c
Integral 9e^12-3t dt
=9e^12-3t / -3
= -3e^12-3t + c
Integral 2x (e^x^2) dx
u=x^2
du/dx = 2x dx
du= 2x dx
dx= du/2x
Integral 2x(e^u)(du/2x)
Integral e^u (du)
=e^x^2 + c
(sec^2 (theta) - sec(theta) tan(theta)) d(theta)
Integral sec^2 (theta) d(theta) - Integral sec(theta) ln(theta) d(theta)
=tan(theta) - sec(theta) + c
Integrals Involving Single Trig Functions:
Integral sin x dx = - cos x + c. Inverse of d cos x / dx = -sin x
Integral cos x dx = sin x + c. Inverse of d sin x / dx = cos x
Integral tan x dx = - ln(cos x) + c. Tan x dx = -d cos x / cos x
Integral cot x dx = ln(sin x) + c. Cot x dx = d sin x / sin x
Integral sec x dx = ln(sec x + tan x) + c
Integral csc x dx = -ln(csc x + cot x) + c as in previous case
Integral sec^2 x dx = tan x + c. Inverse of d tan x = sec^2 x dx
Integral csc^2 x dx = -cot x + c/ Inverse of d cot x = -csc^2 x dx
Trig Integrals
Integral cos (x) dx = sin (x) + c
Integral sin (c) dx = -cos (x) + c
Integral sec^2 (x) dx = tan (x) + c
Integral csc^2 (x) dx = -cot (x) + c
Integral sec (x) tan (x) dx = sec (x) + c
Integral csc (x) cot (x) dx = -csc (x) + c
Integral tan (x) dx = ln (|sec(x)|) + c
Integral cot (x) dx = -ln (|csc(x)|) + c
Integral (1 / (1+x^2)) = tan^-1 (x) + c
Integral (1/ square root 1-x^2) = sin^-1 (x) + c
Integral -4sin (4x) dx
u=4x
dx= du/4
Integral -4sin(u) du/4
Integral -1sin(u) du
-1cos(u)du
cos(4x) + c
Integral x^n dx = x^n+1 / n+1
Integral 3x^-2 dx - Integral 4x^2 dx + Integral 1dx
3(x^-2+1 / -2+1) - 4x^3 / 3 + x + c
= 3x^-1 / -1 + 12x + x + c