Second Midterm, Copy 1

Elementary Calculus Second Midterm, Copy 1 1. Differentiate (1)   Solution: We know (2)   We can use product rule to write (3)     We […]

Power Series

Example 1.   We want to find all numbers for which the power series (1)   converges. Define for every and use Ratio test to write […]

Eigenvalues and Eigenvectors

Example 1.   Suppose we are given the map defined by . We would like to check if is linear. Take two vectors and and write […]

Critical Points

Example 1. Suppose     We would like to find all the critical points of . We know a point is called a critical point of […]

Product & Quotient Rule

Example 1. Suppose we are given     Of course for this problem, we don’t have to use product rule but for the matter of exercise, […]

Arc Length and Curvature Sample Problems

1. Find the length of each curve in space: (1)   (2)   (3)   2. Find the unit tangent vector, principle unit normal vector, curvature, […]