Graph the function 1, x <-1 -1 < x < 0 -x, x = 0 f(x) = 1, 0 < x < 1 x 2 1. -x, 1, Then discuss, in detail, limits, one-sided limits, continuity, and one-sided continuity of f at x =-1,0, and 1. Are any of the dis- continuities removable? Explain.

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

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A: To determine the interval of continuity from the given graphs:

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A: we have to evaluate the limit

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A: Given function, f(x)=1x,      x&lt;1x2,      1≤x≤2-1,      x&gt;2

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A: given : f(x) = 12-x2 to find : slope of the tangent line at (3,3)

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

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Q: lim f(x) given that |f(x)/x² + 1|< 1 x→+∞

A: Recall: Squeeze Theorem for limits:              Assume that functions f,g and h satisfy…

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Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

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Q: Determine the intervals of continuity for the following function. Choose the correct answer below.…

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Q: Discuss the continuity of the function on the closed interval.

A: Given:

Q: the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Given query is to find the slope of the tangent.

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: According to the limit definition of slope: f'(x) is the slope.

Q: Use the definition of continuity and the properties of lim- its to show that the function is…

A: It is given that f(x)=3x4-5x+x2+43 so, when a=2, then we can say that lima→2f(x)=lima→23x4-5x+x2+43…

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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: Suppose that f(x) is a continuous function with f( – 1) = - 8 and f(3) = 8. Determine which choice…

A: Always true

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A:

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Q: Is the function continuous at x = -3? If not, what type of discontinuity occurs? Explain. 6. lim…

A: Given query is find whether function is continuous or not on x =-3.

Q: Discuss the continuity of the function on the closed interval.                               h(x) =…

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Q: Determine if lim f(x) exists. Is the function continuous at x = 2? Show all the steps. f (x) = { 4 S…

A: Given that a function and we check that at x= 2 this function is continous or not . We know that if…

Q: 1. f(x) 2. f(x) = 3. f(x) x² - 4x X 2x x²-9 x² x-2 ; C = 0 -4 ; C = ; C = 2

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Use the definition of continuity, along with the One- sided continuity theorem, to determine whether…

A: We first find left and right hand limit at x=4If left hand limit=f(4)=right hand limit, then the…

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A: We will solve the problem

Q: 3- x, 3. f(x) = [-1,4] 3+x, x > 0 1 4. g(x) [-1, 2] .2 - 4

A:

Q: Suppose that f (x) is a continuous function with f( – 4) = choice best describes the following…

A: Given f(x) is continuous function . And f(-4) =-4 , f(0)=4 . It means f(x) has values of opposite…

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: (-2x + 3, for x<1 S(x) =. x', for xz1 2, ,a=1

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Q: Explain why the function is discontinuous at 4 using definition of continuity. What type of…

A: Given f(x)=x2-x-12x-4 Explain why the function is discontinuous at 4 using definition of continuity.…

Q: Use a table of values to evaluate the limits of the given function

A: Let's find.

Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: a. Determine the value of b to make f(x) continuous at x = -3. Explain your reasoning using limits.…

A: For the function to be continuous value of left limit and right limit should be equal.

Q: Use the function and graph to answer the questions about existence, limits, and continuity. -x-3, -…

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Q: Find the limit of the function, f, as x approaches – 3. x2 – x – 12 - - f(x) = x + 3

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Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The slope of the tangent to the graph 13−x2 by the limit definition.

Q: (2) Determine if each function is continuous at th limits and the definition of continuity. If any…

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Q: For the function f(x)= (8+2x, if x5) A) use definition of continuity at a number (3- step test) B)…

A: Concept: These are the three requirements for continuity: 1). The equation for the function is x =…

Q: f(x)=√√x at x = 7

A:

Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: (x + 1, x 0 Can also be displayed as: x + 1 when x 0 f(x) = Is f(x) continuous at x = 0? Why or why…

A: We have to find the solution of continuity

Q: Use the graph to evaluate the limits. lim f(x) and lim f(x) X→-1- X→- 1+ Ay 2- 1- -5 -4 -3 -2 -1 i 2…

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Q: (- 2x +3, for x 1 0, for x 1 %3D ,a = 1 3.

A: Authoring guidelines:…

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The slope of the tangent line m to the graph of fat the given point x0,fx0 is expressed as-…

Q: Determine the continuity of the function at the given points. forx =-1 %3D f(x = - 2, for x -1 at x…

A: If function f is continuous at x=a then limx→af(x)= f(a)