Calculus 3, Chapter 13 and 14
vector valued function Correct Answer: r(t) = <f(t), g(t), h(t)> =
f(t)i + g(t)j + h(t)k
parameterization:
x = f(t)
y = g(t)
z = h(t)
Limits and continuity of vector valued functions Correct Answer: lim r(t) = <lim f(t), lim g(t), lim h(t)>
t->a
vector equation for the line segment that joins two vectors Correct Answer: r(t) = (1-t)<r0> + t<r1>
Derivative of vector valued function, definition Correct Answer: dx/dt = r'(t) = lim r(t+h) - r(t) / h
h->0
derivative of vector valued function Correct Answer: r'(t) = < f'(t), g'(t), h'(t) >
derivative of dot product [u(t)*v(t)] Correct Answer: u'(t) * v(t) + u(t) *v'(t)
derivative of cross product [u(t) X v(t)] Correct Answer: u'(t) X v(t) + u(t) X v'(t)
integral of a vector valued function Correct Answer: ∫r(t) dt = < ∫f(t)dt, ∫g(t)dt, ∫h(t)dt >
length of a curve Correct Answer: b
L = ∫|r'(t)|dt
a
position, velocity, acceleration Correct Answer: position = r(t)
velocity = r'(t)
acceleration = r''(t)
Projectile Motion - force due to gravity Correct Answer: F = ma = (-mg)j
g = 9.8m/s*s
Projectile Motion - parametric equations Correct Answer: horizontal distance = x = (v0*cos(Θ))t
vertical distance = y = (v0*sin(Θ))t - (1/2)g(t^2)
To create contour maps Correct Answer: set the x,y part of the equation equal to k and solve for y
Limits of multi-variable functions Correct Answer: take limits coming from different directions
Ex: f(x,0) - approach from x-axis
vector valued function Correct Answer: r(t) = <f(t), g(t), h(t)> =
f(t)i + g(t)j + h(t)k
parameterization:
x = f(t)
y = g(t)
z = h(t)
Limits and continuity of vector valued functions Correct Answer: lim r(t) = <lim f(t), lim g(t), lim h(t)>
t->a
vector equation for the line segment that joins two vectors Correct Answer: r(t) = (1-t)<r0> + t<r1>
Derivative of vector valued function, definition Correct Answer: dx/dt = r'(t) = lim r(t+h) - r(t) / h
h->0
derivative of vector valued function Correct Answer: r'(t) = < f'(t), g'(t), h'(t) >
derivative of dot product [u(t)*v(t)] Correct Answer: u'(t) * v(t) + u(t) *v'(t)
derivative of cross product [u(t) X v(t)] Correct Answer: u'(t) X v(t) + u(t) X v'(t)
integral of a vector valued function Correct Answer: ∫r(t) dt = < ∫f(t)dt, ∫g(t)dt, ∫h(t)dt >
length of a curve Correct Answer: b
L = ∫|r'(t)|dt
a
position, velocity, acceleration Correct Answer: position = r(t)
velocity = r'(t)
acceleration = r''(t)
Projectile Motion - force due to gravity Correct Answer: F = ma = (-mg)j
g = 9.8m/s*s
Projectile Motion - parametric equations Correct Answer: horizontal distance = x = (v0*cos(Θ))t
vertical distance = y = (v0*sin(Θ))t - (1/2)g(t^2)
To create contour maps Correct Answer: set the x,y part of the equation equal to k and solve for y
Limits of multi-variable functions Correct Answer: take limits coming from different directions
Ex: f(x,0) - approach from x-axis
