Unit 4 Flashcards
(24 cards)
velocity
derivative of position
says how the object is moving
(+) right/up
(-) left/down
(0) stopped/changing direction
speed
abs value of velocity
acceleration
derivative of velocity
area of a triangle
1/2(base*height)
area of a circle
pi*r^2
circumference of a circle
2pir
dy/dx means
y changing with respect to x
most related rates problems…
some variable changing in respect to time
dz/dt
REMEMBER
if the rate is shrinking put a negative
if something is already a rate…
it is already a derivative
steps to solving related rates problems
- draw a picture and label important variables
- list given information and identify what you are searching for
- find an equation that ties these rates together
- differentiate the equation with respect to time using implicit differentiation
- plug in the values from step one and solve for the unknown
- answer with units and answer any follow up questions
related rates key words…
increasing, decreasing, growing, shrinking, changing
if there are two unknown variables…
find how they relate and replace so only solving for one
position
s(t)
a(t)=0
object stopped/changing direction/moving at a constant rate
can still be moving
speeding up/slowing down
speeding up~a and v have the same sign
slowing down~a and v have different signs
steps to solve motion analysis
- find velocity and calculate the zeroes
- create a sign chart for v
- find a and its zeroes
- create a sign chart for a
- make a motion line using the zeroes of a and v and end points
- decide where the motion is speeding up and slowing down
- make a position graph to show where the particle is and how it moves using the zeroes of v as the x values for s(t)
projectile motion s(t)
-16t^2+V0t+S0
rate of change
rate in-rate out
predicts how a quantity changes over time
equation of a tangent line
L(x)-f(a)=f’(a)(x-a)
where L(x) is the tangent line, f(a) is the original graph, and a is the point at which the tangent occurs
linear approximation says
the y-value of f(x) and the y value of L(x) (the equation of the tangent line at a) will be virtually the same at a.
L’Hospital’s Rule
use when rational limit is indeterminate
finds the limit using the derivatives of num and den
indeterminate forms
0/0, inf/inf, 0^0, inf^inf, 0^inf, inf^0
REMEMBER
write out the lim statement with each step and when dealing with an indeterminate rational limit, write the lim of the num and den separately
