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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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Elementary Calculus, First Midterm, Copy 2
Elementary Calculus, First Midterm, Copy 2 1. Suppose is a given function and and are real numbers. State what we mean by (1) Solution:
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Elementary Calculus, First Midterm, Copy 1
Elementary Calculus, First Midterm, Copy 1 1. Suppose is a given function and is a real number. State what we mean by (1) Solution:
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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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Gram-Schmidt Process
Gram-Schmidt Process, Orthonormal Basis Example 1. We are given the set . First we notice that (1) and therefore the two vectors in this
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Rank and Nullity
Rank and Nullity Example 1. We want to find a basis for the row space of (1) We know the row space of is
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Linearly Independent Sets and Basis
Linearly Independent Sets and Basis Example 1. Suppose we are given the set . We would like to determine if this set is linearly independent.
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Vector Space
Vector Space Example 1. We are given a vector where and are real numbers. We would like to write as a linear combination of vectors and
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