Proof
(a) Prove that
(b) Prove that
(c) Let L be a real number. Prove that if , then
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Proof Prove that if the limit of f(x) as x approaches c exists, then the limit must be unique. [Hint: Let , and , and prove that .]
Proof Let L be a differentiable function for all x. Prove that if for all a and b, then for all x. What does the graph of L look like?
(a) Prove that if , then .
(Note: This is the converse of Exercise 110.)
(b) Prove that if , then .
[Hint: Use the in equality
]