Let 2x - x if 0 4 (a) For each of the numbers 2, 3, and 4, dctcrmine whether g is continuous from the left, continuous from the right, or continuous at the number. (b) Sketch the graph of g.

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A: Graph

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A: It is given that

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A: (b) Given that,f(x)=x+x-1+x-2+x+3+x-4The graph of the function is drawn as shown below.The points of…

Q: -x ifx1 function f. Where is f discontinuous? Justify your answer using the definition of…

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Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: 4x f (x)=- x2 +4 %3D

A: f(x)=-4xx2+4

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A: Here we suppose that the given function is continuous on the given intervals and differentiable on…

Q: Define 1 if x 2 Determine the values of a and b such that f(x) is continuous for all x.

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Q: Define x +3 for x 2 Find a value of c such that g is (a) left-continuous (b) right-continuous In…

A: Answer(a): The given function g(x) is said to be left continuous, if its continuous at x=-1, that is…

Q: Suppose that the function g is defined on the interval -2 if-2<x <-1 -1 if -1<x<0 g (x) = < 0. if 0…

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Q: 1. Sketch the graph off and determine whether continuous at the given value ofc and differentiabl…

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A: The function is not defined at the point x=-3 . Hence the function is not continuous at the point…

Q: Assume whether the function graphed in the accompanying figure is continuous on [-1,3]. y = k(x) 2 3

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Q: consider the function g(x) =   2 − πx         if x ≤ a               x^4              if x > a…

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Q: A function for which f(x) = f( - x) for all x in the domain of f is called a(n) ____function.

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A: Consider the figure:

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Q: f(0) = 0 and f(5) = 2 (ii) f'(x) > 0 if 0 8 f' (x) 0 if 0 8

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Q: Define g(3) in a way that extends g(x) = (x? - 9)/(x - 3) to be continuous at x = 3. %3D

A: Given, g(x)=x2-9x-3

Q: form the graph of f(x) into th 5) f(x) = x³ g(x) = -(x – 2)° %3D 3 %3D

A: We have to find

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Q: Define g(4) in a way that extends g(x) = (x2 - 16)/(x2 - 3x - 4) to be continuous at x = 4.

A: On simplification, we get

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Q: Graph the function

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Q: Define g(4) for the given function so that it is continuous at x= 4. 5x - 80 g(x) = 5х - 20

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Q: Define g(3) in a way that extends g(x) = (x2 - 9)/(x - 3) to be continuous at x = 3.

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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.