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kayvan momeni
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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
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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
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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
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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
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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,
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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,
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