Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the definition of continuity. f(x)={ x² -1 if -22

Q: f(x) : ²+4x-5 a+5 c = - 5

A: The objective of the question is checking the continuity of the given function at given point.

Q: f(x) = 9x² - 4 at x = 1

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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: 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: 3. Analyze the continuity of this function. If there are discontinuities, state the type. x² + 2x…

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Q: Find the value of the constant (a , b, or c) that makes the function continuous.

A: If function is continuous  Then, it will be continuous on x=-1 and x=12 Therefore, limx→-1-1fx=f-1…

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

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Q: is the function f(x) = 1/(x-2) continuous on [1,3]? Justify your answer.

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Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: Determine if the following function is continuous at x = 4. Show all steps by definition of…

A: This question is based on Continuity of function.

Q: Use the definition of continuity to determine whether the shown is continuous at a = 2.

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Q: Use the definition of continuity to decide if the following function is continuous at a = -1. -1.0x²…

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Q: Q3/ A) Decide if the following function is continuous using limits. 2х x1.

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Analyze the continuity of the following function f(x) = 4x + 10      0 ≤ x ≤ 15 at the point x=8

A: The answer is given below:

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

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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: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: (x – 2)2 +1 if x 2

A: We have to check continuity of function at x=0 and x=2

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: To check for the continuity of the function fx=x2+2xx≤14-x1<x<3x-3x≥3

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

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

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Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: It is clear from graph of y=k(x) , that the function k(x) is continuous on the interval [-1,1) and…

Q: Determine whether the following function is continuous at the given point z- 3z+ 14z -5 f(2) 3z -1…

A: A function fx is continuous at x=a if limx→a-f(x) = limx→a+f(x) = f(a)  Given: fx=3x2+14x-53x-1…

Q: where is the function f(x)= llxll-2 continuous (or discontinuous)?

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1<x<3x-3x≥3

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: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Use the definition of continuity to determine whether the shown function is continuous at a = 0.

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Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

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Q: Determine whether the function is continuous at the given points. x+30 if x26 6, 0 if x <6 f(x) = Is…

A: Solution

Q: Use the definition of continuity to show that f is continuous at 2: f(x) = 3x2 – 2x + 1.

A: Definition of function continuity is: A function fx is said to be continuous at point x0 if and only…

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Use the definition of continuity to determine where f(x) is continuous. If it's discontinuous point,…

A: We will solve the problem

Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x²+2x x≤1…

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Q: Consider the function defined by f(x) = -(x + 1)² +5 if x 4 Graph the function. Is the function…

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Q: Give the three conditions that must be satisfied by a function to be continuous at a point.

A: We have to write  the three conditions that must be satisfied by a function to be continuous at a…

Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

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: Q2/B/ check the function continuity at x-0, for the fimction f(x)%= 1+ 4 2/3

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

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Q: Determine if the following functions are continuous at the given value of x. Show your solution. 1.…

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Q: Analyze continuity of the function.

A: Before going to the continuity, we will be finding the domain of the given function. Note that the…

Q: Graph the function

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Q: Determine the continuity and, if discontinous, the type of discontinuity for the function…

A: Given query is to find function is continuous or not at x = -1.

Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

Q: x3-9x f (x) = c = -3 x² +11x+24

A: Given function is fx=x3-9xx2+11x+24. To determine whether function is continuous at c=-3. Solution:…

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.