Sketch a graph of a single function that has all of the following propertie a) Continuous and differentiable for all real numbers, b) f '(x) >0 on (-3, -1) and (2, ), c) f (x) <0 on (-, -3) and (-1, 2), d) f "(x) > 0 on (-∞, -2) and (1, ), e) f"(x) < 0 on (-2, 1), ) f'-3) =f (-1) =f (2) = 0, g) f"(x) = 0 at (-2, 0) and (1, 1).

Q: (3-х, х <2 +1, x 2 2 B. Is the function h(x) continuous at x-2?

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Q: 2. Let f(x) = Determine the exact location of any turning points. Use the second derivative to…

A: We can solve this as follows:

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A: For (a),

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A: Here we use the concept of limit

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A: given function :

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Q: Limit x approaches to minus infinity under root 5-x

A: Property used: limx→∞f(x)=limx→∞f(x) Some properties of ∞: ∞+a=∞∞b=∞∞=∞

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A: Since you have submitted two questions, we'll answer the first question. For the second question…

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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.