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Squeeze theorem


We want to find limx0xsin(x). Direct substitution and other algebraic methods don't seem to work.
Looking at the graph of f(x)=xsin(x), we can estimate that the limit is equal to 1.
To prove that limx0xsin(x)=1, we can use the squeeze theorem.
Luke suggested that we use the functions g(x)=x+1 and h(x)=x+1 in order to apply the squeeze theorem.
Does Luke's suggestion seem to be correct?
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