Calculus…yeah.

EZ vocab

100

A slope of a tangent line at any point. 

What is a derivative 

200

(d/dx)∫f(x)dx=F(b)-F(a)

(integral is from a to b)

What is the Fundamental Theorem of Calculus(FTC)

300

approximates used to approximate a function, find the anti derivative of a complicated function, or compute an otherwise un computable sum.

What is a Maclaurin series?

400

π∫[f(x)]^2dx

integral is from a to b

disk method

500

name all five and the general name for all to get full points. All sigma are from 0->∞

∑a_n…diverges if lim n->∞ a_n≠0

∑1/n^p

∑(-1)ⁿa_n(a_n>0)

∑a_n for a_n=f(n)

∑ar^n-1

nth-term or test for diverges, p-series, Alternating series(AST), Integral test, Geometric series. These are the Tests for Convergence

Stuff you should memorize

100

0/0->

Indeterminate

200

d/dx(cscx)=

-csc(x)(cot(x))

300

∫(1/√(1-x²)dx

arcsin +C

400

∑sin(X)

∑(-1)ⁿ(x²ⁿ⁺¹/(2n+1)!)

500

f(x)=L/(1+e^-k(x-x₀)

logistic function

Derive deez

100

(dy/dx)(sin³(x))=

3sin²xcosx

200

if arcsinx=ln(y), then dy/dx=

y/(√(1-x^2)

300

What is the slope of the tangent line to the polar curve r=1+2sinø at ø=0

1/2

400

f(x)=3/(2x²-7x+5) find slope and critical points of f int he interval 1<x<2.5

-15/4 is the slope of tangent line

x=7/4 is abs max

500

If f(x,y,z)=e^xylnz, then find f_x(x,y,z)

f_x(x,y,z,)=e^xy/z

integrate deez

100

∫(5x+8)/(x²+3x+2)dx

from 0 to 1

ln(18)

200

∫xe^{-x^2}dx

from 1 to ∞

1/2e

300

∫sin²(x)cos⁴(x)dx

x/2+(sin4x)/8+C

400

∫(4x²-3x+2)/(4x²-4x+3)dx

x+(1/8)ln(4x²-4x+3)-(1/(4√2))arctan((2x-1)/√2))+2

500

∫((x^2)/(x²+1)^3/2)dx

(x/√(x²+1))+C

Rules

100

Power rule for derivative u*v

what is u' v +  u v'

200

Quotient Rule for derivative u/v

What is (u' v - v' u)/v^2

300

What is the rule of integration for exponential function?

What is ∫(e^x) dx = e^x + C 

400

What is ILATE stand for in integration?

Inverse trigonometric function

Logarithmic function

Algebraic function

Trigonometric function

Exponential function

500

When can we apply L'Hopital's rule (min. 3)

if the function is:

0/0                       inf/inf                1^inf

0^0                      inf  -  inf

0 . inf                   inf ^0