KOREA UNIVERSITY
2019 Calculus II (MATH 162-22) Sample Exam 1
1. Find the curvature at each point of the ellipse
(Solution)
Let’s write a parametric equation of the ellipse as cos
cos sin
′ sin cos Then ′
sin cos
′ ×″ sin cos .
acos sin
′ ×″
So the curvature
′ sin cos
2. Find an equation for the level curve of the function through the given
point .
passing through the given point .
(Solution)
2019 Calculus II (MATH 162-22) Sample Exam 1
1. Find the curvature at each point of the ellipse
(Solution)
Let’s write a parametric equation of the ellipse as cos
cos sin
′ sin cos Then ′
sin cos
′ ×″ sin cos .
acos sin
′ ×″
So the curvature
′ sin cos
2. Find an equation for the level curve of the function through the given
point .
passing through the given point .
(Solution)
