calculus

math trivia/history

100

the study of how things change

what is calculus?

200

newton and leibniz

who are the people who discovered calculus?

300

the study of mathematical symbols and the rules for manipulating these symbols

what is algebra?

400

what is the only even prime number?

two

500

how many seconds are in one day?

86,400 seconds

rules/theorems

100

The method for finding limits of indeterminate forms

what is l'hopital's rule?

200

if f(x)= g(h(x)), then f'(x)= g'(h(x))*h'(x)

what is the chain rule?

300

f'(c)= (f(b)-f(a))/(b-a)

what is the mean value theorem?

400

if f is an integrable function and if g(x)= ∫f(x)dx

then ∫_a^bf(x)dx= g(b)-g(a)

(note: sorry the formatting is weird)

what is the first fundamental theorem of calculus?

500

d/dx ∫_a^x f(t) dt= f(x)

what is the second fundamental theorem of calculus?

math problems

100

find the first derivative of y= -2(1+x)⁴

y'= -8(1+x)³

200

solve:

lim_(x-->2) (x³−7x²+10x)/(x²+x−6)

−1.25

300

evaluate:

∫(6x⁵−18x²+7)dx

x⁶−6x³+7x+c

400

∫ ₀⁵  (2x + 1)dx

30

500

if g(x)= (6x²)/(2−x) then find g'(x)

g'(x)= (24x−6x²)/((2−x))

misc./terminology

100

0/0 and infinity/infinity

What are indeterminate forms?

200

the instantaneous rate of change of f(x) at x=c

what is a derivative?

300

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?

400

the value that a function approaches as the input approaches some value

what is a limit?

500

what is the derivative of lnx?

1/x