se a graph to determine whether the given function is continuous on its domain. g(x) =    7 − x if x ≤ 7 x + 7     if x > 7 continuousdiscontinuous     If it is not continuous on its domain, list the points of discontinuity. (If there is no such point, enter NONE)

Q: (9 pts.) Determine if the following function is continuous at x=-2. If not find the type of the…

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Q: Sketch the graph off. At each point of discontinuity, state whether f is left- or right-continuous.

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Q: Give an example of a function ƒ(x) that is continuous for all values of x except x = 2, where it has…

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Q: 3. State where the function below is continuous using interval notation. if x<2 4 f(x) = 3 if x 2

A: To check whether the given function is continuous using interval notation.…

Q: G(x)= x³ +3x+2 x+2 [[x]] + 1 -1-x-21 - 4 x+3 + 1 x-r if x<-1 if -1 ≤ x 1 if xz1

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Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

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Q: Test continuity for the following function : x < 0 f(x) ={-x3 1 0 < x <1 1< x < 2 1 X = 2

A: A function f(x) is continuous at x=c, if the left-hand limit, right-hand limit, and the value of the…

Q: -2x+6 Consider the function f (x) = x3+2x2-15x

A: Here we use basic definition of function.

Q: (5) State the value(s) of x where the functions are discontinuous (x = a) AND the type qf…

A: Given that, fx=1               if x&lt;2x+3         if 2≤x≤47              if x&gt;4

Q: ere is the function decreasing linterval notetion)

A: Given query is to find the interval where function increasing and decreasing.

Q: b) Find the Constants "a" and "b" such that the following function is continuous for all real…

A: We have to properties of continuity first.

Q: Is the following function continuous? x2 – 9 if x 3 if x = 3

A: The function is given by

Q: Is the function continuous or discontinuous? If discontinuous, what condition is not satisfied?

A: Given:

Q: Consider the function on graph. Analyze the continuity of this function (continuous or…

A: Consider the function on graph.

Q: Identify three cases for a function NOT to be differentiable at a. Explain why each case fails the…

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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.