Unit 4 Quick Quiz Calculus

Position

s(t)

Velocity

s’(t) or v(t)

Acceleration

s’’(t) or v’(t)

v(t) < 0 means the particle is…

moving left or down

v(t) > 0 means the particle is…

moving right or up

Average Velocity

(s(b) -- s(a))/(b-a)

Speed

|Velocity|

If velocity and acceleration have the same sign…

the particle is speeding up

If velocity and acceleration have different signs…

the particle is slowing down

Local Linearity

The tangent line of the function f(X) at x = a can be used to approximate the value of f(x) for points close to x=a.

A function that is Concave Up indicates…

It is an underestimate

A function that is Concave Down indicates…

It is an overestimate

Assume that g'(x) doesn't equal 0 for all x in (a,b), except possible at c itself. If the limit of f(x)/g(x) as x approaches c produces the form 0/0, then...

Limit as x--> c for f(x)/g(x) is equal to limit as x --> c of f'(x)/g'(x), provided the limit on the right exists or is infinite., also is applicable to any of indeterminate forms. ∞/∞, (-∞)/∞, ∞/(-∞) or (-∞)/(-∞)