By the definition show that f(x) = 2 + |x| is a continuous graph at the origin. Also, show the result graphically.

Q: Carefully sketch the graph of a continuous function f which satisfies the following properties:

A: Given, Sign of f'x-f'x<0 on an interval -∞,-2. f'x>0 on an interval -2,0. f'x<0 on an…

Q: The graph of f is given above. Which statement regarding the local (or relative) minimum of f is…

A: Relative minima is the point where slope of the graph is zero and there is a change from negative…

Q: g(x) = at x = 2 %3D x+2

A: Definition of continuous function helps to check whether the given function is continuous or not. A…

Q: for the quartic function represented by this graph?

A: In the given question, the concept of quartic function is applied. Quartic Function A quartic…

Q: Find the open intervals on which the function is increasing or decreasing.        y = x + 9/x

A: To find the critical points we solve dy/dx=0

Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

Q: sketch to graph the function f(x) = In(x + 2) – 1. %3D

A: f(x)=ln(x+2)-1Now, putting value of x=-1f(-1) =ln(-1+2)-1           [ln1=0]           =0-1…

Q: Given the graph below, what can you say about the function at x = -2? -10 Not Continuous Continuous

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Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: Use the graph to determine open interval on which the function is decreasing, if any.

A: From the given graph, it is observed that the graph of the function is decreasing in the left side…

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

A:

Q: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

Q: Sketch the graph of f (x) = x |x|. Then show that f'(0) exists.

A: If f(x) is a continuous function, then derivative of the function at point a exits if and only if…

Q: = Find a continuous function

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Q: Suppose that the function y=f(x) is decreasing on the intervals (8,3) what can be said about the…

A: Question is solved.

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

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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: Sketch the graph of the floor function f(x) = x+ 1| over the interval [-3, 3) %3D Show your work

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Q: Consider the graph of f' (x). At what value (or values) of x do f (x) have a local maximum?

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Q: Find the intervals on which f(x) = x(x + 3)(x – 1) is positive by plotting a graph. (Enter your…

A: Given - A function To Find - Interval for f(x)>0

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: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: 4. Which of the following functions is a piecewise-defined continuous function? For the…

A: Given, The graphs of  Functions of A , B, C and D  Continuous functions : Continuous functions are…

Q: Give three characterizations of what it means for the graph of f (x) to be concave up at x = 2.…

A: Consider the given information as The graph of fxto be concave up at x=2. Concave down.

Q: find the intervals on which f(x) is increasing and decreasing. then sketch the graph. f(x) = 7 --…

A: We use first derivative to find out where function increasing or decreasing  when f'(x)<0 then…

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: Suppose f is a continuous function on [a,b] and suppose that f(a) 0 What can you say about the…

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Q: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

Q: Sketch a continuous graph with the following conditions f'(x) 0 if (-4, 4) • f"(x) > 0 if (-0o, –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: 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: Sketch a graph of the piecewise defined function.

A: We have to draw the graph of function fx=1-x2,      if x≤2x       ,      if x>2   Graph for…

Q: 1.Find the domain for the continuous graph below.

A: Domain of function is that values of x for which graph is spread at x-axis

Q: Sketch the graph of a continuous function on [0, 2] forwhich the Trapezoidal Rule with n = 2 is more…

A: The midpoint rule is a method of finding the area under a curve. We use the midpoint of each…

Q: Find and label as minimum or maximum the stationary points for: f(x)-x -20х+105

A: We will solve the problem

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

A: To sketch the graph if a function f which is continuous on (-∞, ∞)  and first and second derivatives…

Q: 2) If possible, give an example of where a function is continuous at a point but not differentiable…

A: Continuity of a function is the characteristic of a function by virtue of which, the graphical form…

Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then…

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.

Q: Sketch the graph of f'(x) for f(x) = x³ + x³ . Label at least 3 points on this graph .

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Q: Use the graph to determine the values of x at which the function is not continuous.   x=

A: Given the graph of the function

Q: (4) Is it possible to define a function which is continuous on a closed, finite interval but does…

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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 piecewise defined function.

A:

Q: If f : [0, 3] → R is continuous, must its range be a closed interval?  use the continuous map

A:

Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: y=2x-sin2x The domain of given function is -∞, ∞. The range of sin2x is -1, 1.

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

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. 3 -4 -2…

A: According to company policy we are allowed to provide solution for only first 3 sub parts. If you…

Q: Select all of the graphs that depict a function which is not differentiable at x=0.

A: Here, we need to select all the graphs that depict a function which is not differentiable at x=0.…

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.