Question: Given: Let f ( x ) = 2 x + 3 be a function from the real numbers to the real numbers.

Task:

1. Find the set of δ values that satisfy the formal definition of \[\underset{x\to 4}{\mathop{\lim }}\,f(x)=11\] given the value ε = 0.1, showing all work.
2. Demonstrate that \[\underset{x\to 4}{\mathop{\lim }}\,f(x)=11\] by using the formal definition of the limit, showing all work.
3. Prove the theorem that if \[\underset{x\to d}{\mathop{\lim }}\,h(x)=P\] and \[\underset{x\to d}{\mathop{\lim }}\,k(x)=Q\] and h ( x ) ≥ k ( x ) for all x in an open interval containing d , then P ≥ Q by using the formal definition of the limit, showing all work.

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document