Briefly explain what the Mean Value Theorem tells us. Why do we require that f be a continuous function in order to apply this theorem? You may sketch a graph to explain your reasoning.

Q: 10 (0.103, 5.051) (-0.843, 0) |(-0.277, 0) (1.307, 0) (3.61, 0) (4.537, 0) -1 2 3 4 5 -5 --10 (3.23,…

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Q: For a curve to be symmetric about the x-axis, the point (x, y) must lie on the curve if and only if…

A: Consider a curve symmetric about the x axis.Then the point (x,y) lie on the curve if and only if the…

Q: (a) f(x) 15 for x < 2 for x ≥ 2

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Q: Use a graph to explain why. if f is defined at x = a.

A: The given integral is ∫aafxdx Formula used: it is known that the area bounded by the graph of fx and…

Q: 1 point Would the following data represent a function? y 4 3 3. 3. O Function Not a Function 5.

A: definition of a function is: a relation from a set of inputs to a set of possible outputs where each…

Q: Determine the value the constant a for which the function g(x) is continuous at x=1 9(x)=√x² +5x + 2…

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Q: What is a function, in your own words? Give an example to back up your points.

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Q: What is the range of the relation shown below? O 0Sy<4 O 0 < y<4 O 0<y< 4

A: Graph of the function is given and we have to find the range of the function.

Q: b) f(x) = -4x³ – 6x² + 24x + 1 Use the first derivative test to determine the intervals where the…

A: Use the first and second derivative of the function for increasing/decreasing and concavity.…

Q: Can a graph of a function be symmetric about the r-axis (do not consider a special case of a line y…

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Q: В С -10-2 -6 -2 1 5 13 2 69 3x + 2y = 4 >+ X

A: We have to find out

Q: 18+x Find the absolute extrema of the function f(x) = on the interval [6,9]. %3D 18-x Find the…

A: See the attachment

Q: it a function

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Q: Use the vertical line test to identify graphs in which y is a function of x ?

A: a). Now let us draw a vertical line on the given curve, we get Clearly the vertical line passes…

Q: On the previous page, we learned how to use the graph of a function to determine where the function…

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Q: 27. g(x) = 2x² - x - 15 x - 3 1 kx - if x # 3 if x = 3

A: Explanation of the answer is as follows

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.