Discuss the continuity of the following function: 2* (1- x), x<0 f(x) = {1-a, x² - x +1, x>0 x < 0 x = 0

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

Q: Axample 2 3. Use the definition of continuity to prove that the function is not continuous at x =-5.…

A: Given query is to prove that function is not continues at x = -5.

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: Discuss the continuity of f(x) = 2x + 3 at x = −4.

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Q: Discuss the continuity of the function

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Q: Define f(x) = (x2 - 81)/(x - 9) at x = 9 so that the function becomes continuous at 9.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Discuss the continuity of the function on the closed interval.                              g(x) =…

A: We can not have a negative value under the square root.  So,

Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the…

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Q: Define f(x) =(x2 - 81)/(x - 9)at x = 9 so that the function becomes continuous at 9.

A: Given function is fx=x2-81x-9. To define function fxso that the function becomes continuous at x=9.…

Q: Determine if the following function is continuous at x = 4. Show all steps by definition of…

A: This question is based on Continuity of function.

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x&lt;5x+1            ,  x≥5

Q: The definition of the first derivative of a function f(x) is: Select one: f(x+Ax)-f(x) a. f'(x) =…

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Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

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Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Use the definition of the derviative to compute the derivative of f(x)=1−3x2f(x)=1−3x2 at the…

A: Use the definition of the derivative to compute the derivative of f(x)=1−3x2 at the specific point…

Q: (x2 + 3x f(x) = 3 – 6x if x -2 Check the continuity of the function f(x) at x = -2

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Q: Discuss the continuity of the function on the closed interval.

A: Given:

Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: Find the points at which the function f (x) is continuous and the points at which f is…

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Q: fully continuous for all x E R by use of the product rule differentiate the function f{x} = x3e-4x

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Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

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Q: Determine if the piecewise function is continuous at a. x-3 x + 3 f(x) = 1, x-3 a = 3 x = 3 O Yes,…

A: Topic- limit

Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: Discuss the continuity of the function on the closed interval.                               h(x) =…

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Q: Discuss the continuity of the composite function h(x) = f(g(x)).

A: To discuss: The continuity of the function hx=fgx. Given: The functions are  fx=tan x and gx=x2.…

Q: Sketch the graph of a continuous function y =f(x) that satisfies the following conditions: 1. f'(x)…

A: This question is about graphing a function

Q: Determine if the given function is continuous at a given value of x. 2. f(x) = x² - 4x – 2 at x = 1…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: At what points are the functions continuous x -X- g(x) = X - 3 y " 5, x = 3

A: Given:  1. 2.

Q: 2. Let f(x) =- 3-2x Use the definition of the derivative to find f'(x). Show complete work,…

A: The given function is f(x)=x23-2x.

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: 3- x, 3. f(x) = [-1,4] 3+x, x > 0 1 4. g(x) [-1, 2] .2 - 4

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Q: Examine whether or not the function (4-x² f (x) =- [4+x if x0 Is continuous at x = 0

A: Check whether limx→0f(x) = limx→0(4-x2) and limx→0(4+x), if both sides are equal then it is…

Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

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Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

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Q: function

A: We are given a function : f(x)=x2-2x+2x-3 We have to determine the domain of given function where…

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

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Q: 6. Which of the following is the reason for a function differentiable at x=-5 if the function is…

A: Since this is a multiple question according to the Bartleby answering rule, only first question is…

Q: Discuss the continuity of the function on the closed interval.                             Function…

A: The given function is said to be continuous in a closed interval [a,b] if it is continuous in (a,b)…

Q: Discuss the continuity of the function f(x) = {x^2 - 3x         if x &lt; 2           {2x + 4…

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Q: Discuss the continuity of the function. x2 – 4 f(x) X + 2 f is discontinuous at x =

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Q: Discuss the continuity of the function on the closed interval.                        Function g(x)…

A: Givengx=1x2−4  Interval [-1,2]

Q: • Example 2 What can you say about the continuity of the function f(x) = 9 – x??

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Q: The derivative of a function of f at x is given by provided the limit exists. f'(x) = lim h→0…

A: We can use the given definition to find the derivative as below.

Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: Suppose f(x) is differentiable everywhere and f(-3) Show f(1) > -6 and f(-5) -2.

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Q: Sketch a possible graph of a function that satisfies the given conditions. f(-2) = 2 lim f(x) = 1…

A: Step:-1 Given that  f(-2)=2limx→-2-f(x)=1limx→-2+f(x)=-1 f is continuous but not differentiable at…

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Q: Determine the continuity of the function at the given points. forx =-1 %3D f(x = - 2, for x -1 at x…

A: If function f is continuous at x=a then limx→af(x)= f(a)

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.