Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE.) f(x) = x2 − 10x + 25/x − 5; a = 5

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A: Given the characteristics of the graph of a function:

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A:

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A:

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A:

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Q: Q2) Find the open intervals on which the function is increasing and decreasing f(x) =/4-x %3D

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A: The given function is

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A: Here, given function is: f(x)=12-12exx

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A:

Q: Example 1: The function has a removable discontinuity at 2. How would you redefine f(2) to make f…

A: Given: also, this function has a removable discontinuity at 2.   To determine: redefine f(2) to…

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A:

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A:

Q: sketch a possible graph of a function f that satisfies the following conditions: i) f'(x) > 0 for x…

A: topic - functions

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A: We need to find a.

Q: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f…

A:

Q: 3-64 -If f(x)=04 is the function continuous at x=4 x-4

A: If a function f(x) is given and we have to check continuity at x=a then we have to find LHL, RHL and…

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

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A:

Q: Find the values of xER for which the function given below is both defined and continuous. f(x) = In…

A: f(x)=ln(x-9)Since f(x) is log functionIt is defined for all( x-9)&gt;0⇒x&gt;9

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A: To check whether the function is continuous or discontinuous calculate the limits as shown Now…

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A:

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A: 1-  Given- fx=1+x+2 To Sketch- The graph of the above function and determine whether it is…

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A: Follow the next step

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A:

Q: 3 Sketch a graph of the function f(x) = ax(x + 3)°(x – 1) , for some positive constant a. -

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A: Consider the given function f(x)=x2+x-2x-1; x≠1            =    k          ; x=1 The function break…

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A: We will solve the problem.

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing.…

A: solution is given by

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A: Given graph of f' is,

Q: Let f(x)=(x-3)/(x2-1).  What can you say about the long-term behavior of f?

A:

Q: What can be said about f (3) if f is continuous andlim f(x) = ½? x→ 3

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A:

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

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A: sketch the graph Graphically Explanation Since the graph of the function is not break at any point.…

Q: Shown below is the graph of f(x) defined on the closed interval –2 < x < 6. f(x) -1 |0 4 6. Which of…

A:

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A: For the given statement

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A:

Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

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A: Given  g is an odd function and let h=f∘g. To find  Is h always an odd function? What if f  is odd?…

Q: Find the domain of the below function: g(x)=In(x-x²)

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A:

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A: f(x)=x2(x+2)(x-1)2(x-2)

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. ​f(x)=6−x2

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A: Here given function as fx=-19x3-3 Differentiate with respect to x f'x=ddx-19x3-3=-39x2=-13x2 Thus…

Q: The function f given by f(2) = { if a 3 -2x+15 is continuous at = 3

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Q: Suppose that f(x) is continuous. The table below shows intervals where f'(x) and f"(x) are positive,…

A: graph is given below..

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.