formula test study

integration by parts

what is IVT?

The Intermediate Value Theorem (IVT) states that if a function is continuous on a closed interval , it must take every value between and at least once, meaning for some in . It guarantees the existence of a root or solution within an interval

What is EVT?

What is MVT

Rolle’s Theorem

first derivative test for max/min

secon derivative test for max/min

displacement is ?

the integral of velocity

total distance travelled

integral of the absolute value of velocity

speed is

|velocity|

how to know if speed is increasing or decreasing

average rate of change

slope

instantaneous rate of change

derivative

when f’(x)=0

f(x) has a max or min

when f’’(x)=0

this is a point of inflection on f(x)

what is a point of inflection

where the concavity changes

volume by washers

diffy q seperation of variables steps

Euler’s method

MVT formula

MVT formula for integrals

average value

displacement

integral of velocity

distance travelled

integral of |velocity|

final position

initial position + integral of velocity

area Between Curves

Integral of top- bottom or integral of right - left

volume of known cross section

disk method formula

shell method

arc length (rectangular)

surface area

harmonic series

1/n

limit of a sequence

nth term test

shows only divergence

the integral test

p series test

error Bound for integral test

direct comparison test

limit comparison test

alternating series test

define absolute convergence

conditional convergence

how do we estimate the sum of a convergent alternating series

ratio test

root test - this is not tested but could be helpful