Unit 1
area formula of a circle
Pi*r2
what is the derivative of a constant?
0
what is the dirivative of the integral of x2
vise versa?
x2
x2+c
integral of a-b (f(x)dx=F(b)-F(a)
what is Kallies favorite color
purple or yellow
volume formula of a cylinder
Pi/3*hr2
f'(x)*g(x)-f(x)*g'(x)/g(x)2
what shape do we use to calculate the area under the curve?
rectangles or trapizoids
What is MVT and IVT?
Mean value theorem and Intermediate value theorem
how many times did we say we were going to drop the class and then never did?
every day since the semester started, close to 500 probably multiple times a day tbh
what are types of discontinuity?
holes jumps vertical asyptotes
what is the dirivative of ax
ln(a)*ax
What can you do to check if your integral was right?
take the derivative of your answer silly
Formula for integral of chain rule
integral of F'(g(x))*g'(x)dx=F(g(x))+c
how many times did we have to work on the boards this semester
too many, close to 200 probably
what makes a function continuous?
lim must exist, function is defined, lim value=function value
what is the limit definition of a derivative
lim [f(x+h)-f(x)]/h
h->0
what does first derivative test(fdt) test for?
local extrema
How do you evaluate a definite integral?
ex: integral from 1-3 of x2-9
take integral then plug in b and a and subtract
ex:
1/3x3-9
-26/3
How many days have we had calc this semester?
75 on friday
if the right and left side "agree" is the function continuous?
yes they are married for life, no divorce over here
what is the derivative of f(x)=3tan(6x)+sec(18x)
f'(x)=18tan(6x)+18sec(18x)tan(18x)
if f(x) is increasing (1,3)U(5,7) decreasing from (3,5) and concave up (1,7) what does the graph look like
look at kallies answer sheet
Tn=1/2*delta x[f(x1)+2*f(x2)...+f(xn+1)]
ET<(or equal to) [(b-a)3/12n2]*M
who was the og host of Jeopardy?
Art Fleming