Example: Sketch a graph of a function that has a removable discontinuity at x = -2, a jump discontinuity at x = 1 but is continuous from the right at x = 1.

Q: Is the function f graphed below is continuous at = -4? Choose the appropriate reason that justifies…

A: topic - continuity and limits f is not continuous at x =-4 reason = left hand limit is not equal to…

Q: DETERMINE WHETHER THE GIVEN FUNCTION m(x) IS CONTINUOUS OR DISCONTINUOUS AT x = -1

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

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: Suppose g is a continuous DECREASING function on the interval [-3,1].

A: 2. As y is a continous decreasing function on the interval -3, 1

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: Sketch the graph of a function f that is continuous except that is has a removable discontinuity at…

A:

Q: Sketch the graph of a continuous function f that satisfies all the stated conditions: f(0)=4,…

A:

Q: 2. State whether each function in question 1 is continuous or not. If not, state where it is…

A: Definition of the continuous function is, Right hand side limit and Left hand side limit should be…

Q: Consider the piecewise function below. (1/x, x 2 f (x) = x2, -1, Where is it discontinuous? Label…

A: Given function, f(x)=1x,      x<1x2,      1≤x≤2-1,      x>2

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

A: Given data: The absolute maximum at MA=5. The absolute minimum at mA=2. The local maximum at MB=3.…

Q: Sketch the graph of a function f that is continuous except for the stated values(s). Discontinuous,…

A: The function is discontinuous at x=3 and right continuous at x=3

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: Give an example of a function ƒ(x) that is continuous for all values of x except x = 2, where it has…

A:

Q: Sketch the graph of a function that is continuous on (- 00,00) and satisfies the following set of…

A: Given that, the graph of a function that is continuous on (-∞, ∞) and satisfying the following set…

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

A:

Q: Sketch the graph of a function that is continuous exceptfor the stated discontinuity. Neither left…

A:

Q: In Exercises 1–4, say whether the function graphed is continuous on [-1, 3]. If not, where does it…

A: Domain = -1, 3Concept - For a graph or a function to be continuous, the function should give a value…

Q: In The given question, , determine whether the statement is true or false. If it is false, explain…

A: we have to tell whether the given statement is true or false. Statement : If a function is…

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A:

Q: We informally describe a function f to be continuous at a if itsgraph contains no holes or breaks at…

A: Continuous function: A function fx is said to be continuous at point c if the following conditions…

Q: { -2x + 3 x 1

A: We have given a piecewise define a function fx which definition change at x=1. The functions…

Q: Given the graph below, what can you say about the function at (-1,1)? Not Continuous Continuous

A: The graph of a function is said to be continuous if the value of the function exists for all values…

Q: 3. Sketch the graph of a function f(x) that is continuous except for the stated discontinuity. a).…

A:

Q: (b) Redefine f(4) so that f is continuous at x = 4 (and thus the discontinuity is "removed"). f(4) =

A: The given function is: f(x)=x2-12x+32x-4

Q: Sketch the graph of a function that is continuous exceptfor the stated discontinuity.   Removable…

A: Given: The graph has a removable discontinuity at 3 and jump discontinuity at 5.

Q: The graph of a function f is given. y 1 1 Determine whether fis continuous on its domain.

A:

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: Create a graph of the following function to determine whether it is continuous on its domain. S-a +…

A: From the basics of Limits and Continuity

Q: Sketch a continuous graph with the following conditions f'(x) 0 if (-4, 4) • f"(x) > 0 if (-0o, –1)…

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: 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: 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.

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

Q: Consider the graph of a function f on the interval [0, 4).

A: We have to conclude about local extreme value of f from the graph.

Q: 4 3 sketch graph of a function that is continuous on (-infinite,infinite) and has the following…

A: To make a sketch of the graph of the function  with given differentiable properties

Q: Which of the following is a function that has a jump discontinuity at x = 2 and a removable…

A:

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: Sketch the graph of a continuous function f if the graph of f' appears as in Figure 5 and f(0) = 0.…

A:

Q: Which of the following functions has a horizontal asymptote at y =-?

A: Here, the objective is to find the horizontal asymptote of the function.

Q: The function whose graph is given below is discontinuous at x = 1 because the third condition of…

A: A function f(x) is continuous at a point c  if and only if the following three conditions are…

Q: Sketch the graph of a function f that is continuous except for the stated discontinuity.…

A:

Q: draw the graph of a function f on [0, 4] with the given property. Jump discontinuity at x = 2 and…

A: Draw the graph for the given conditions as follows. Sketch the graph of the function with jump…

Q: Sketch the graph of a continuous function f which satisfies the following properties.

A: Given,

Q: Sketch the graph of a continuous function that satisfies the following conditions: f'(x) > 0 on (–…

A: Given information f'x>0 on −∞,2f'x<0 on 2,∞f''x>0 on −1,1f''x<0 on −∞,−1 and 1,∞ We have…

Q: Sketch the graph of an increasing function such that f'' (x) changes from + to − at x = 2 and from −…

A: Sketch the graph of an increasing function such that f”(x) changes from + to - at x = 2 as follows.

Q: Given the graph below, what can you say about the function at x = -1? Continuous Not Continuous

A: Explanation of the answer is as follows

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

A: Given, Graph of the function f(x) is continuous on-∞,∞ y=f(x) and has the following…

Q: Sketch the graph of a function f that is continuous except for the stated discontinuity. The…

A: Removable and jump discontinuity

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.