If f is continuous on (−∞, ∞), what can you say about this graph?

Q: f is continuous iff f-1(E) is closed

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Q: Sketch the graph of a function that is continuous on an open inter-val (a, b) but has neither an…

A: Suppose, f(x) is any function and its graph is drawn as:

Q: If f is continuous on (-o, co), what can you say about this graph?

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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: Sketch the graph of a function f  that is continuouson [1, 5] and has the given properties.   f has…

A: f is continuous on [1,5]. f has no local maximum or minimum. 2 and 4 are the critical numbers.

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: If f is differentiable at a number, x, then f is continuous at x.

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Q: use the formal definition of limit to prove thatthe function has a continuous extension to the given…

A:

Q: use the formal definition of limit to prove that the function has a continuous extension to the…

A: Given function is fx=x2-1x+1 and point is x=-1

Q: Write a delta - epsilon proof that shows that the function f(x) = 3x – 5 is continuous at æ = 2

A: Let ε>0 be given. Also let 0<δ<min1,ε3. Then for x-2<δ,…

Q: Use limits to determine if f(x) = is continuous at z = -2. (z+2)²

A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: 9-x - S(x)= Vx- 6

A:

Q: Suppose that f has a one-sided limit at each point of fa, b. Prove that f is bounde

A: In mathematics, a function f defined on some set X with real or complex values is called bounded if…

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Prove that the following function is continuous on the interval [-5,5]: H(x)= the square root of…

A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

Q: Sketch the graph of a functionf that is continuous except for a removable discontinuity at 2.

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Q: use the formal definition of limit to prove that the function has a continuous extension to the…

A: Recall the formal definition of the limit to prove the result as follows: limx→3fx=limx→3x2-2x-32x-6…

Q: Let f : X → Y be a continuous function. If X is disconnected then so is f(X). True False

A: Let f : X → Y be a continuous function. If X is disconnected then so is f(X).

Q: Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).

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Q: If f is continuous on (-x, ∞), what can you say about its graph?

A: If f is continuous on (-oo oo) what can you say about its graph?

Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

A: Let us consider a continuous function fx=cosx for x∈0,2. fx is continuous on 0,2 Now, exact value of…

Q: Show that ( if f is decreasing is riemann)

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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: Use the definition of continuity and the properties of limits to show that the function is…

A: A function is continuous in an interval if is continuous on every point of the interval. Now, a…

Q: Suppose fx) is a continuous function. Then a function F(x) Such that F'(x) =f{x) is called:

A: Given:- Suppose f(x) is a continuous function Then a function F(x) F'(x) = f(x) is called

Q: What is the continuous extension of f(x) = x3-1 at point x-1. %3D x2-1'

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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 algebraically if f is continuous at x= 0.

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Q: Suppose f′(x) is continuous with f(9)=8 and f'(9)=-12. Calculate the following limit or determine…

A: Answer and explanation is given below

Q: Define f(2) in a way that extends f(s) = 2 to be continuous at s = 2. %3D -4

A: The function is defined as fs=s3-8s2-4.

Q: Determine if g (r)= is continuous at a = 8.

A:

Q: Let f(x) = −2/x and g be the function defined b)Is f . g continuous at x = 3? If not, does…

A: limit of the composite function

Q: Graph h and describe the discontinuity: for x 0 Is h left- or right-continuous?

A:

Q: 1. f (x) = 3x² + 2x + 1 at x = -2

A: Given that:                            1. f(x)=3x2+2x+1                 at x=-2.2. h(x)=x+1x2-1 at…

Q: use the formal definition of limit to prove that the function has a continuous extension to the…

A:

Q: Compute the limit as x approaches zero of f(x)=(x^2+3x)/(x^2-x-12)

A: Given : Function f(x)=(x2+3x)(x2-x-12)   To find : Limit of given function when x approaches to…

Q: Suppose f" is continuous on (-o, 0). (a) If f'(2) = 0 and f"(2) = -2, what can you say about f? (b)…

A: Application of derivative problem

Q: sketch the graph of a function that is continuous everywhere except at x=3, and is continuous from…

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Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: Suppose f(x) is a continuous on the interval [a,b] and c is a number in (a,b). If f"(c) is…

A: If f(c) is a local maximum then f''(c) &lt; 0 and if f(c) is a local minimum then f''(c) &gt; 0

Q: If f(x) is a function such that the limit of f(x) as x approaches a does not exist, then f(x) is not…

A: Let's find.

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

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Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

A:

Q: draw the graph of a function f on [0, 4] with the given property. Infinite one-sided limits at x = 2…

A:

Q: Show that the following statement is false by drawing a graph that provides a counterexample: If 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.