Assume f(x) is continuous on (-infinity,infinity) Use the given information to sketch the graph of f

Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws of…

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Q: Use interval notation to indicate where f(x)=x-7/(x-5)(x+5) is continuous.   "f" is continuous on…

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Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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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: (b) f(x) - (x + 2x')', a- -1

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Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: On which interval is the function f(x) = tan x² continuous Is the function f(x) = ! - continuous at…

A: 3.1)  tan x2 =sin x2cos x2We know that sin x2 and cos x2  are both continuous functions.Thus, tan…

Q: Explain, using the theorems, why the function Is continuous at every number In Its domaln. x- 9 Q(x)…

A: Given: Q(x)=x-93x3-9 To find: The domain and Why the function is continuous at every number in its…

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Note that the domain of g(x) is all real numbers and the domain of h(x) is also all real numbers. So…

Q: nuous

A: The function f is continuous at some point c of its domain if the limit of f(x), as x approaches c…

Q: What conditions must be satisfied by a function if it is to be continuous at an interior point of…

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Q: Determine whether f is continuous on its domain. If it is not continuous on its domain, say v…

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Q: use interval notation to indicate  where f(x)=x-7 divided by (x-2)(x+1) continuous  f is…

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

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

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Q: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x<1           x…

Q: f(x) = (x + 2x³)“, , a = -1 %3D

A: Limits Limit of the function at point a exists if and only if  left hand limit and right hand limit…

Q: Determine whether f is continuous or not at x = 2. Justify your answer and state your conclusion.…

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Q: Determine if the given (picture attached) is continuous or not at x = 1 and at x = 0.  Identify the…

A: Heavy check the continuity at x = 0 and x = 1 then we identify the discontinuity.

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

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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 that f is a function satisfy |f(x)|<=|x| for all x. Show that f is continuous at f = 0.…

A: Suppose that there is a function f that satisfies

Q: Determine if the given (picture attached) is continuous or not at x = -1. Identify the type as…

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Q: How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to…

A: Given : fx = x2-x-2x-2

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: Determine algebraically if f is continuous at x= 0.

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Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

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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: 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: 11. ((x) – (x + 2r'), a--1

A: To find the limit.

Q: Use the definition for continuity to determine whether the function continuous at x= 1 and x= 2?

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Q: Assume f is continuous on an interval containing zero anddifferentiable for all x not equal to  0.…

A: Consider the Darboux Theorem: Let I be an open interval, f:I→ℝ, a real- valued differential…

Q: Show that f(x) has a removable discontinuity at x = 0 and determine what value for f(0) wou make…

A: Given that ,  fx=9x+-8x+9xx-1if x≠0 and x≠13if x=0 We know that, A function fx is said to have…

Q: Use the definition of continuity and the properties oflimits to show that the function…

A: Consider the given function as fx=x16-x2

Q: Let f be a function that is continuous on the closed interval [1, 5] with f ( 1) = 10 and f (5) =…

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

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Q: The graph of the function f'(x) of a continuous function f is shown. On what intervals is f concave…

A: It is given that,the graph of the function f'(x) of a continuous function f.  We have to find…

Q: The table below gives for the value of continuous function f at each x-value. Using the Intermediate…

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Q: f(x) = X-5 if xŹ 2 at x = 2 2x if x< 2

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

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Q: Determine the set of points at which the function is continuous

A: f (x, y, z) = sin-1 (x2 + y2 + z2) = t (Let's say)Hence, sin t = (x2 + y2 + z2)

Q: Determine at which points, the function 97× ナ x²if x E RIQ f(x)= is continuous.

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Q: Determine whether f is continuous on its domain. If it is not continuous on its domain, say why. 4F…

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Q: Explain the difference between a function f(x) being continuous at the point x=a and the limit…

A: We need to find the difference between function is continuous at x=a and limit exists at x=a

Q: Sketch the graph of f.  Then identify the values of c for which the limit f(x) exists as x-->c.…

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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: Determine whether f is continuous on its domain. If it is not continuous on its domain, say why. 1…

A: Need to find continuous and discontinuous of function

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.