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In each of the following exercises, we shall use the notation f(x) to denote the function x→f(x), x ε R. In each case, V will denote the vector space of all real-valued functions on the real line, with the vector operations defined point-wise. In each case, determine whether or not the given set is linearly independent and compute the dimension of the linear subspace spanned by the set.
18. {1, eax, ebx}, a≠b.23. {1, cos2x, sin2x}.
Elimination or substitution methods
describe applications of the cartesian coordinate system to plot a real-world situation. in your description indicate
Loan amortization, which refers to determining equal annual loan payments, can be implemented by which of the following?
Solution of an absolute value equation
Find the value of x by the properties of logarithms.
For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly.
Find the solution to the system for linear equation by using the given equation.
Solve the vertex and axis of symmetry from the graph.
The amounts on the arcs represent the maximum daily amount sofwater that can flow across the network in thousand sofgallons. Determine the maximum amount of water that can flow through the system.
Asymptotes for rational functions: f(x) = P(x)/Q(x). Given the formula, reconstruct a rational function based on the following pieces of information.
What is the relationship between exponents and logarithms? How would one distinguish between the two, using both a graph and a sequence?
Use elimination method to solve the problem.
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