252Calculus: IntroductiontoVectorValueFunctions by: javier

252 Calculus: Introduction to Vector Value Functions

by: javier

Calculus Redo Limits: Then and Now

Calculus Redo: Limits: Then and Now

THEN y is a function of x

Calculus Redo: Limits: Then and Now

THEN y is a function of x y = f(x)

Calculus Redo: Limits: Then and Now

THEN y is a function of x y = f(x)

NOW each cordinate is a function of t, and t is called the parameter. x =x(t) = t y =y(t) = t2 z =z(t) = 3

Calculus Redo: Limits: Then and Now

THEN Plot f(x) = x2

Calculus Redo: Limits: Then and Now

THEN Plot f(x) = x2 y

x

Calculus Redo: Limits: Then and Now

NOW Plot⃗r(t) = ⟨t, t2 , 3⟩

THEN Plot f(x) = x2 y

z

x

y x

Limits: Then and Now

First Semester: Limits

Now: Limits

Limits: Then and Now

First Semester: Limits sin(x) x→∞ x lim

Now: Limits

Limits: Then and Now

Now: Limits

First Semester: Limits sin(x) lim x→∞ x

⟨ lim

t→∞

sin(t) 3t , , cos t 1+t

( )⟩ 1 t

Calculus Redo Derivatives: Then and Now

Derivatives: Then and Now

First Semester: Derivatives

Now: Derivatives

Derivatives: Then and Now

First Semester: Derivatives if f(x) = 3x2 + 5x then d (f) dx

Now: Derivatives

Derivatives: Then and Now

First Semester: Derivatives

Now: Derivatives

if f(x) = 3x2 + 5x then

if r = ⟨3t2 , 5t + 1, sin(t)⟩ then

d (f) dx

d (r) dx

Calculus Redo Integrals: Then and Now

Integrals: Then and Now

First Semester: Integrals

Now: Integrals

Integrals: Then and Now

First Semester: Integrals if f(x) = 3x2 + 5x then ∫

fdx

Now: Integrals

Integrals: Then and Now

First Semester: Integrals

Now: Integrals

if f(x) = 3x2 + 5x then

if r = ⟨3t2 , 5t + 1, sin(t)⟩ then

∫

∫

fdx

rdt

Calculus Redo Product Rule: Then and Now

Product Rule: Then and Now

First Semester: Product Rule

Now: Product Rule

Product Rule: Then and Now

First Semester: Product Rule d(f · g)

Now: Product Rule

Product Rule: Then and Now

First Semester: Product Rule d(f · g)

Now: Product Rule d(⃗u · ⃗v)

Product Rule: Then and Now

First Semester: Product Rule d(f · g)

Now: Product Rule d(⃗u × ⃗v)

Typical Questions given ⃗g, find⃗r

given⃗g, find⃗r Suppose ⃗g = ⟨0, −9.8⟩ find the position vector function,⃗r

given⃗g, find⃗r Suppose ⃗g = ⟨0, −9.8⟩ find the position vector function,⃗r

given⃗g, find⃗r Suppose ⃗g = ⟨0, −9.8⟩ find the position vector function,⃗r

if ⃗vo = ⟨40, 10⟩ and ⃗ro = ⟨0, 5⟩ find⃗r

given⃗g, find⃗r Suppose ⃗g = ⟨0, −9.8⟩ find the position vector function,⃗r

if ⃗vo = ⟨10 cos(20o ), 10 sin(20o )⟩ and ⃗ro = ⟨0, 5⟩ find⃗r

Typical Questions given⃗r, find⃗v and⃗a

given⃗r, find⃗v and⃗a Suppose⃗r = ⟨5 cos(3t), 5 sin(3t)⟩

⃗v ⃗a ⃗r

□ find⃗v

given⃗r, find⃗v and⃗a Suppose⃗r = ⟨5 cos(3t), 5 sin(3t)⟩

⃗v ⃗a ⃗r

□ find⃗v □ find ||⃗v||

given⃗r, find⃗v and⃗a Suppose⃗r = ⟨5 cos(3t), 5 sin(3t)⟩

⃗v ⃗a ⃗r

□ find⃗a

given⃗r, find⃗v and⃗a Suppose⃗r = ⟨5 cos(3t), 5 sin(3t)⟩

⃗v ⃗a ⃗r

□ find ||⃗a||

Homework Questions anything...

Homework Questions anything...

anything...

anything...

anything...

anything...

anything...