y = g(x) 2 1. 2 3

Q: Find the x -values (if any) at which f(x) is not continuous, where (x-5

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Q: (9 pts.) Determine if the following function is continuous at x=-2. If not find the type of the…

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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 interval (s) where the following function is continuous x-7 f(x)= (x-7)x+4)

A: In the given function (x-7) is a common factor in numerator and denominator. So, it will cancel out…

Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a.…

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: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

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Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: For what value of a is the following function continuous at every x?

A:

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)>0 then function increasing when f'(x)<0 then function decreasing

Q: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

Q: For what value of c is the function defined below continuous on (-∞, )? сх + 4, x 4. x > 4. f(x) = C…

A: f(x) = cx+4    ,  x<4cx2-4  ,  x≥4we have to check continuity on (-∞ , ∞)for a function to be…

Q: Find the constant a such that the function is continuous on the entire real line. (x) = {4x?, ах —…

A: We have to find a

Q: Determine using the given graph if the function f is continuous on the following intervals. 2. 1. a.…

A: Let's find.

Q: Determine the interval(s) on which the following functions are continuous. x + óx + 17 flx2 = x² - 9

A: Given The function is

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

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Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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Q: Determine if the given function is continuous on the given interval a. [2,5) , x <O f(x) = %3D 5x-8…

A: To determine whether the given function is continuous on the given interval.Interval=[2, 5)fx=1x,…

Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: The graph of a function is said to be continuous in an interval if there is no break in ite graph at…

Q: Describe the interval(s) on which the function is continuous.

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

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

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Q: The graph of a continuous function f : [0,9] → R is given below. The function

A: given F(x)=∫0xf(x)dx

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: It is clear from graph of y=k(x) , that the function k(x) is continuous on the interval [-1,1) and…

Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

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Q: At what points are the functions continuous?

A: The part of the function -x2 / 2 is always continuous. There is no point of discontinuity here. The…

Q: For what value of k is the following a continuous function?

A: Function is continuous if   limx→2-f(x)=limx→2+f(x)=limx→2f(x)

Q: For what value of k will the function f be continuous on (-0,0)? x² –100 f (x) = { * if x + -10 =…

A: Continuous function should not have any abrupt (sudden) changes.

Q: Determine if the given function is continuous at a given value of x.

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

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: Determine whether the function is continuous at the given points. x+30 if x26 6, 0 if x <6 f(x) = Is…

A: Solution

Q: Find values of the constants k and m, if possible, that will make the function f continuous…

A: If f is continuous at x=a then limx→a-fx=limx→a+fx=fa . Assume , f is continuous every where to find…

Q: draw the graph of a function on [O, 5] with the given properties. f is left-continuous but not…

A: f is left-continuous but not continuous at x=2, and right-continuous but not continuous at x=3. Let…

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

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: Find a value for the constant k, if possible, that kæ? if x 2 Is the function f(x) = 1 continuous…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and | g(2x)dx = 12. 2 | #g(3x²)dx. Find

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Q: Which of the following does not represent a function that is continuous everywhere?

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Q: Show whether the following function is continuously differentiable: f(x,y)=x2y2

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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: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A:

Q: For what value of a is the function continuous at every x?

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Q: Sketch a graph of the function f that is continuous on (- o0,00) and has the following properties.…

A: First, we need to satisfy that f'(x)&gt;0. So, the function must be an increasing function. So, the…

Q: 5. Find the value of k that makes the following function continuous. f(x) : ={2x - 1,if x2-1

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Q: Find the values of a and b such that the following p Function is continuous at points -2 and x-5…

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.