3. Suppose that f is continuous on the interval [0,1] and that f(0) > 0 and f(1) < 1. Use the Intermediate Value Theorem to show that f has a fixed point on [0,1]. That is, show f(c) = c for some c in [0,1]. (MAKE SURE YOU CHECK ALL CONDITIONS BEFORE APPLYING THE IVT)

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Q: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: Please comment if you need any clarification. If you find my answer is useful please put thumbs up.…

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A: See the attachment

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A: The function is defined as fs=s3-8s2-4.

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

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A: We want to prove the given result.

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A: According to the problem, we have

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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.