Korea University
2019 Fall
Calculus 2 (Exam 1) 2019. 10. 12
Name : Student ID : Major:
** Show all your work to get the full credit. There are 10 problems, and each problem is worth
10 points. No calculators are allowed during our exam.
1. Find an equation for the level curve of the function through the given point .
2. Find the length of the curve
cos sin ≤ ≤
3. Find an equation of the tangent plane to the given surface at the specific point.
4. Find and of the function
5. (a) Find the linear approximation to the function sin at the point
.
(b) Use the answer in (a) to estimate .
6. Let sin .
Find , if is defined implicitly as a function of and by the equation .
7. Use the Chain Rule to find at if
ln
8. Calculate the curvature at each point of the following curve
9. Find parametric equations for the tangent line to the curve at the point , where the
curve is an intersection of two surfaces and .
10. Find of the function .
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2019 Fall
Calculus 2 (Exam 1) 2019. 10. 12
Name : Student ID : Major:
** Show all your work to get the full credit. There are 10 problems, and each problem is worth
10 points. No calculators are allowed during our exam.
1. Find an equation for the level curve of the function through the given point .
2. Find the length of the curve
cos sin ≤ ≤
3. Find an equation of the tangent plane to the given surface at the specific point.
4. Find and of the function
5. (a) Find the linear approximation to the function sin at the point
.
(b) Use the answer in (a) to estimate .
6. Let sin .
Find , if is defined implicitly as a function of and by the equation .
7. Use the Chain Rule to find at if
ln
8. Calculate the curvature at each point of the following curve
9. Find parametric equations for the tangent line to the curve at the point , where the
curve is an intersection of two surfaces and .
10. Find of the function .
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