ACTIVITY 1: CONTINUITY AND DIFFERENTIABILITY Direction: Apply the concepts that you have learned from continuity and differentiability to answer the given question. Is the function defined by: x-3 if x 2, f(x) = x2 +1 if x > 2. continuous at x = 2? differentlable at x = 2?

Q: Activity 1: Determine whether the given functions are continuous, differentiable, neither, or both…

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Q: f(x) = x^2 - 4 / x + 2   1. Describe the interval(s) on which the function is continuous. (Enter…

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Q: cos( (b) Test the continuity of the function f(x) = x-2 at the point x = 2. x = 2 4'

A: A function f is said to be continuous at x=a if both left hand limit and right limit exist at x→a…

Q: II. 1. Sketch the graph of fand determine whether continuous at the given value of c and…

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Q: Duestion:- For what of value the constant "<' is on (-o, 00 ? the function continuous f(x)={ -" if…

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Q: generate a continuous and differentiable function f(x) with the following properties: f(x) is…

A: Given: f(x) is decreasing at x=−6 f(x) has a local minimum at x=−3 f(x) has a local maximum at x=3

Q: O g(x )= ( % x + %); X so , at the point X,=O. x >0 9x - X

A: To check the continuity, we will see the limit of the function at x=0  and the function value at x=0…

Q: In Exercises 37-40, draw the graphs of each of the piecewise-defined functions. when x 0 37. f(x) =

A: Hey, since there are two questions posted, we will answer the first question. If you want any…

Q: constant k is the functionf defined by if x +0 f(x) = V5- x - V5+x k if x = 0 continuous at x = 0?…

A: On putting limit x tends to 0 when condition of not equality it becomes 0/0 form . So by…

Q: For the linear functions given below, provide an answer for each topic (when appropriate). If the…

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Q: Label true or false if: 1. If f(x) is increasing and f(x) > 0 on the interval I, then g(x) =…

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Q: Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the…

A: The given functiopn,   f(x)=x3+8x-9

Q: Find the absolute maximum and minimum values of the following function on the given interval. If…

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Q: Use the graph of the derivative f ′ of a continuous function f is shown. (Assume f ′ continues to…

A: NOTE: Refresh your page if you can't see any equations. .

Q: . If f(x) = x + 1, then %3D (a) the value of f at x = -1 is f(–) : %3D (b) the value of f at x = 2…

A: We have to fill in the blanks: If fx=x3+1, then a the value of f at x=-1 is f ____=______. b the…

Q: X-2 6. f(x) = V*+3 %3D

A: Given- fx=x-2x+3 To find- The values of the x for which the above function is continuous.

Q: (x? + 3x f(x) = - 6x if xs-2 if x>-2 A) Check the continuity of the function f(x) at x = -2 %3D

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Q: Current Attempt in Progress x + 18x + 81 Find a value of x, if any, at which f(x) = - is not…

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Q: 1. Consider the graph of the function f(x) = 1.a. Is the function f (x) continuous at x = 1? Justify…

A: We need to find if the function is continuous or not in given interval.

Q: The graph of the derivative f' of a function fis shown. y= f'(x) 2 (a) On what intervals is…

A: See the attachment

Q: S-2x f(x) = x2 Discuss the continuity of the given function at x=0. If discontinuous, is f(- x>0…

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Q: A function f(x) decreases by 10 over every unit interval in x and f(0): = -1. Which could be a…

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Q: ACTIVITY 1: Determine if the following functions are continuous at the given value of x. If the…

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Q: 7x-1 if x 4 If f(x) is a function which is continuous everywhere, then we must have %3D

A: For the function to be continuous the value of left limit of x at 4 should be equal to right limit…

Q: Find the absolute maximum and minimum values of the following function on the given interval. If…

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Q: Consider the function f(x) =    2 − πx        if x ≤ 0              x^4              if x > 0 .…

A: We will use the fact i)For function at a point if the left hand limit is not equal to right hand…

Q: Generate a continuous and differentiable function f(x) with the following properties: f(x) is…

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Q: generate a continuous and differentiable function f(x) with the following properties: f(x) is…

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Q: Find the points of inflection of the graph of the function. (Order your answers from smallest to…

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Q: 3. Determine if the given function is continuous on the given point and intervals. 3x - 5, f(x) =…

A: Given: f(x)=3x-5x≤-12x2+5x-1&lt;x&lt;13x3-2x≥1with a. a=1b. [-1, 1]c. (-∞, 0]

Q: 2) Is the function f given below continuous at a = -2? Explain. Show all the work to get a full…

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Q: Using the definition of monotonicity prove that the function f(x)=x2+1 is strictly increasing for…

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Q: Identify a function f that has the given characteristics. f(–4) = f(2) = 0;  f '(-1) = 0,  f '(x)…

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Q: consider the following function  f(x) =2x/x-7 describe the local behavior of the function f(x) is…

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Q: x 2) Discuss the continuity of the graph of f(x) given below on the closed interval [-4, 2] D(-4,6)…

A: This question is related to continuity of functions, we will solve it using given information.

Q: Find the absolute maximum and minimum values of the following function on the given interval. If…

A: We find the critical numbers by solving f'(x)=0

Q: Justify your answer whether the following functions are continuous or not at a certain point or…

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Q: Q) Test the continuity of the function f(x): 3 - x X + 1 2Sx <3 3S X< 4 F(x) = 2х —1 X = 4

A: Use limit method

Q: A. (a) Sketch the graph of the function given (b) Determine if it is continuous at x, (c) Identify…

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Q: Activity 1. The discussion of the concept of continuity is already done. It is now time for you to…

A: A rational polynomial function y=fxgx is continuous everywhere except such x where gx=0. Given: 1).…

Q: (c) Simplify the function f(x) = |x – 1| + |x + 1|. Test the continuity of this function at x = 1.…

A: From the given information. The function f(x) is as follows.

Q: find value of  A if f(x) is continuous at x=2 if  f(x)={x−1,x<2            {ax+3,x≥2

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Q: Determine the continuity of the following functions. Determine continuity, if applicable. the kind 9…

A: To check the continuity of the given functions.

Q: Find the absolute maximum and minimum values of the following function on the given interval. If…

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Q: Q#2. Give an example of functions f and g , both continuous at x = 0 for which the composite fog is…

A: There doesn't exist any function. Because

Q: onsider the following function. A.) Find f(2). B. Is f(x) continuous at x=2? Why?

A: Given data: The expression for the given function is f(x)=3x2+7,      x&gt;25x-1,        x≤2 A)…

Q: A. (a) Sketch the graph of the function given (b) Determine if it is continuous at x, (c) Identify…

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Q: A. (a) Sketch the graph of the function given (b) Determine if it is continuous at x, (c) Identify…

A: We will make graph piecewise. One for x&lt;=0 and other for x&gt;o.

Q: x -9 (a) f(x) = 고-7x-30

A: The solution is given below in the next step:

Q: The graph of the derivative f' of a function f is shown. X 2 4 8 10 2 14 16 18 (a) On what interval…

A: The given graph is of f'x.We need to find the intervals on which f is decreasing, on which f is…