Math 126 Midterm 1 Exam comprehensive
questions fully solved & updated (Latest Update
2026) UPDATE!!
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Practice questions for this set
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T(t) = r'(t) / ‖r'(t)‖
Choose an answer
1 Unit Tangent Vector 2 Arc Length/Distance Travelled
Find the domain and range of
3 4 Unit Normal Vector
g(x,y) = √(9-x²-y²)
Don't know?
Terms in this set (40)
Arc Length/Distance Travelled L = s(t) = ∫ ‖r'(t)‖dt = ∫√[(dx/dt)²+(dy/dt)²]
, Reparametrizing a Curve 1) Integral using arc length formula -> solve
for t and replug in
2) set a random variable = t (e.g. x=t)
Curvature - measures how "bent" a curve is
- measures how the direction of the tangent
is changing
- rate of change of T(t) wrt arc length
- make a circle around the curve
- smaller radius of that circle = more
curvature
Osculating Circle - R = 1/curvature
- smaller radius = more curvature (bentness)
-Same tangent as curve at P
- lies toward which N points
Unit Tangent Vector T(t) = r'(t) / ‖r'(t)‖
Unit Normal Vector N(t) = T'(t) / ‖T'(t)‖
- Points in the direction in which the curving
is turning at each point
Binormal Vector B(t) = T(t) × N(t)
- Osculating plane's normal vector
- To determine B(t) direction, use RIGHT
HAND RULE
questions fully solved & updated (Latest Update
2026) UPDATE!!
Save
Practice questions for this set
Learn 1 /7 Study with Learn
T(t) = r'(t) / ‖r'(t)‖
Choose an answer
1 Unit Tangent Vector 2 Arc Length/Distance Travelled
Find the domain and range of
3 4 Unit Normal Vector
g(x,y) = √(9-x²-y²)
Don't know?
Terms in this set (40)
Arc Length/Distance Travelled L = s(t) = ∫ ‖r'(t)‖dt = ∫√[(dx/dt)²+(dy/dt)²]
, Reparametrizing a Curve 1) Integral using arc length formula -> solve
for t and replug in
2) set a random variable = t (e.g. x=t)
Curvature - measures how "bent" a curve is
- measures how the direction of the tangent
is changing
- rate of change of T(t) wrt arc length
- make a circle around the curve
- smaller radius of that circle = more
curvature
Osculating Circle - R = 1/curvature
- smaller radius = more curvature (bentness)
-Same tangent as curve at P
- lies toward which N points
Unit Tangent Vector T(t) = r'(t) / ‖r'(t)‖
Unit Normal Vector N(t) = T'(t) / ‖T'(t)‖
- Points in the direction in which the curving
is turning at each point
Binormal Vector B(t) = T(t) × N(t)
- Osculating plane's normal vector
- To determine B(t) direction, use RIGHT
HAND RULE
