A fixed point of a function f is a number c in its domain such that f(C)=c (The function doesn't move c; it stays fixed) (A) Sketch the graph of a continuous function with domain [0,1] whose range also lies in [0, 1]- Locate a fixed point of f (b) Try to draw the graph of a continuos function with domain [0, 1] and range in [0, 1] that does not have a fixed point. What is the obstacle? (c) Use the intermediate value theorem to prove that any continuous function with domain [0, 1] and range in [0, 1] must have a fixed point.

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Q: 3 х 1 (x² – 1

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Q: A fixed point theorem

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.