math trivia/history
the study of how things change
what is calculus?
The method for finding limits of indeterminate forms
what is l'hopital's rule?
find the first derivative of y= -2(1+x)4
y'= -8(1+x)3
0/0 and infinity/infinity
What are indeterminate forms?
newton and leibniz
who are the people who discovered calculus?
if f(x)= g(h(x)), then f'(x)= g'(h(x))*h'(x)
what is the chain rule?
solve:
lim(x-->2) (x3−7x2+10x)/(x2+x−6)
−1.25
the instantaneous rate of change of f(x) at x=c
what is a derivative?
the study of mathematical symbols and the rules for manipulating these symbols
what is algebra?
f'(c)= (f(b)-f(a))/(b-a)
what is the mean value theorem?
evaluate:
∫(6x5−18x2+7)dx
x6−6x3+7x+c
1. f(c) exists,
2. lim(x-->c) f(x) exists, and
3. lim(x-->c) f(x)=f(c)
when is a point continuous?
what is the only even prime number?
two
if f is an integrable function and if g(x)= ∫f(x)dx
then ∫abf(x)dx= g(b)-g(a)
(note: sorry the formatting is weird)
what is the first fundamental theorem of calculus?
∫ 05 (2x + 1)dx
30
the value that a function approaches as the input approaches some value
what is a limit?
how many seconds are in one day?
86,400 seconds
d/dx ∫ax f(t) dt= f(x)
what is the second fundamental theorem of calculus?
if g(x)= (6x2)/(2−x) then find g'(x)
g'(x)= (24x−6x2)/((2−x))
what is the derivative of lnx?
1/x