Andrew Deppe Final Calculus Project

Limits

100

$100 What is a limit?

The value that a function approaches as that function's inputs get closer and closer to some number.

200

$200  google slide

limit = 0 and f(-2) = -4

300

$300  google slide 

positive and negative square route of 2

400

$400  google slide

f(8)= -2 and the limit at f(8) = 5.

500

$500  google slide

the limit from the left is 14. The limit from the right is 7 and the general limit does not exist. 

Derivatives/Antiderivatives

100

$100 Take the second derivative of 4x³ - 8x + 2 

24x

200

$200 Take the derivative of 12x¹³ - 3x²+1

156x¹²-6x

300

$300 Take the antiderivative of 5x⁴-2x³+6

x⁵-1/2x⁴+6x+C

400

$400 Take the second derivative and antiderivative of 4x⁷-6x²+12x

2nd derivative: 168x⁵-12

anti : 1/2x⁸-2x³+6x²+C

500

$500 Take the antiderivative of the antiderivative of 3x⁵-9x³+2x+4 (second antiderivative) 

F(x)= 1/14x⁷-9/20x⁵+1/3x³+2x²+C(1)x+C(2)

Summation

100

$100 google slide

74

200

$200 google slide

-36

300

$300 google slide

-95

400

$400 google slide

30

500

$500 google slide

2515

Integrals

100

$100 google slide

20.25

200

$200 google slide

0

300

$300 google slide

75

400

$400 google slide

-5,397.6

500

$500 google slide

-3.33333333333333333333333333333

Implicit Differentiation

100

$100 Take the derivative of x² + y²=4x³

dy/dx = 64x^2 - 2x / 2y

200

$200 Take the derivative of 3x³+y²=y²+4

dy/dx = DOES NOT EXIST (dy/dx's cancel)

               

300

$300 Take the derivative of x^2 y + xy^2 = 3x

dy/dx = 3 - 2xy - y^2 / X^2 + 2xy

400

$400 Take the derivative of x²+y²=9

!!!!!!!!!!!!!!DAILY DOUBLE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
dy/dx= -2x / 2y

500

$500 Take the derivative of        x³ + x² y + 4y² = 6

dy/dx = -3x^2 -2xy / x^2 + 8y