(b) Determine the discontinuities of the following functions and state why the function fails to be continuous at those points. Check your answers by using a graphing calculator ( such as Desmos) F(x) =x2-3x-10/x+2

Q: f(x) = 9x² - 4 at x = 1

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

A: for being a contrinuous function this condition should be satisfiedlimx→a-f(x)=limx→a+f(x)=f(a)from…

Q: Determine the discontinuities of the following functions and state why the function fails to be…

A:

Q: Find the value of the constant (a , b, or c) that makes the function continuous.

A: If function is continuous  Then, it will be continuous on x=-1 and x=12 Therefore, limx→-1-1fx=f-1…

Q: The function f is continuous for all real numbers, and the graph of y = f'(x) is given. (a) Does the…

A: Given y=f'(x) is the function of the graph  a)Horizontal tangent lines: From the graph, we get the…

Q: At what points is the following function continuous? x2 - 4x -5 x+5 f(x) = x- 5 6, x = 5 ..... The…

A: At what point is the function continuous

Q: Find numbers a and b, or k, so that f is continuous at every point. 5) f(x) = 10x + 8,if x < -1 kx…

A: If f is continuous , solimx→-1-fx=limx→-1+fx

Q: Find the domain of f(x) = 3x/(x − 1) and discuss the behavior of f near any excluded x-values.

A: Given function is f(x)=3xx-1 Since domain is the set of all those input values for which the…

Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: How to determine whether the function is continuous or not at a given point x = a ? x ≤ 1 (3x5 - 1…

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Q: Determine if the following functions are continuous at the given value of x. Show your solution. 1.…

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

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: b. Determine the discontinuities of the following functions and state why the function fails to be…

A:

Q: S(x + 4)² -2 < x x < -2 f(x)

A: fx=x+42    -2≤xx2              x&lt;-2 Since the given function is a polynomial function for all…

Q: Find number k, so that f is continuous at every point. 3x+9, if x-6

A: Given,  fx = 3x+9   if   x&lt;-6kx+6   if  x ≥ -6  fx is continuous at every point, then we have to…

Q: Given f(x) is a continuous function. If f( – 5) = 1 and f'(x) > 4 for – 5 <x < 2, what is the…

A:

Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

A:

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

A:

Q: The function fis continuous for all real numbers, and the graph of y = f'(x) is given. (a) Does the…

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Q: Find the intervals on which the function is continuous. x+5 y = (x-4)(x-3) (х-4)(х-3)

A: y is continuous on (−∞,3)∪(3,4)∪(4,∞)

Q: For the function g(x) in part (c), how would you "remove the discontinuity"? In other words, how…

A: First, we find limx→3g(x). We rewrite g(x) as, g(x)=(x-3)(x-1)(x-3) If x≠3 we have…

Q: Is the functionf graphed below is continuous at x= -1? Choose the appropriate reason that justifies…

A: Continuous at x=-1, as limit is equal to f(-1).

Q: what is the mathematical condition for the function to be continuous at a certain point c?  is the…

A: A  function is said to be comtiuous at a point x=c , in its domain if the following three conditions…

Q: 1. From the graph, determine the function f (x) is continuous at x = -1. f(x) 3 %3D %3D -5 -4 -3 1…

A:

Q: Give an example of a function g(x) that is continuous for all values of x except x = -1, where it…

A: Consider the figure:

Q: If function g(x) =- is discontinuous at x=a, find the points of (x-a) x2 -1 (x+4)(2x-3)´…

A:

Q: The piecwise function g(x) is defined by x + 2 when x 1. What type of discontinuites are present in…

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Q: What is f (3) When x²-9 X-3 f(x) = x when XX3? Assume that f(x) is a function that is continuous for…

A:

Q: Find the value of k so that the function 5x +3 if x< 3 f(x) = - kx2 is continuous everywhere? if x23

A: we have to find the value of k where f(x) is continuous everywhere  Also find the domain in the next…

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

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Q: Find the x-value at which the function is not continuous. Are any of the discontinuites removeable?

A: Find the function is removable or non-removable discontinuity.

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: Find the numbers at which the function is given   is discontinuous. At which of these points is f…

A:

Q: Suppose f'(x) < 2 for all x 2 2, and f (2) = 7. Show that f(4) < 11.

A: Given that f'x &lt;2 for all x≥2 and f2=7.We need to show that f4&lt;11.

Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

Q: SBx? - з (Bx + 2 if Suppose that f(x) = x > 2 if Find the value of ß so that f(x) is continuous…

A: For continuity, left hand limit=right hand limit=f(x)

Q: Find a value of the constant k, if possible, at which kx2 f(x) = x+k x> -7 is continuous everywhere.…

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Q: The piecewise function f(x) is defined below. f(x) = {kx² - 4, Is-2 x+ 2, xS-2 x>-2 For what value…

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Q: What type of discontinuity is present in the function 3x – 2 if r 2 O The function has a removable…

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Q: What kind of discontinuity does f(x) = *-3 have at x = 2? X-2

A: A function is said to possess non-removable discontinuity if the limit of the function does not…

Q: (b). Determine whether the function is continuous or discontinuous at the given x-value. x²-3 x=-5…

A: Given function is

Q: 3 b) Find values of x, if any, at which f is not continuous:f(x) =+2

A:

Q: On what intervals is the function f(x) = x-4r both decreasing and concave up? Write your answer in…

A: fx=x4-4x3 Differentiating with respect to x, we get f/x=4x3-43x2    ∵dxndx=n·xn-1=4x3-12x2 Again…

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: Given, fx = x2-2x-3x-3  We have to define f3 in order to make f is continuous at 3.

Q: x3-9x f (x) = c = -3 x² +11x+24

A: Given function is fx=x3-9xx2+11x+24. To determine whether function is continuous at c=-3. Solution:…

Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…

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.