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

Q: Describe the interval(s) on which the function f(x) = is continuous.

A: The given function fx=xx2+x+2 is in gxhxform. The numerator gx=x is continuous for all x∈-∞,∞ in its…

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

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Q: Determine the discontinuities of the following functions and state why the function fails to be…

A: f(x)=x3+x2-17x+15x2+2x-15function is undefine when x2+2x-15 is become 0Let…

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: Find the values of a and b that make the following piecewise defined function both continuous and…

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Q: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

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Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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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 the points where the given function is not defined and is therefore not continuous. For…

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Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

A: Given the statement that " Will a function that is differentiable on a given interval always be…

Q: Determine where the function f(x) is continuous.

A: The given function is , fx =x-8

Q: Determine whether the function is continuous or discontinuous 5. f(x) =

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Q: b) State what it means for a function to be continuous at a point x = a.

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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: Find the values of a and b that make f continuous everywhere.

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Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

Q: What points is the function y=|5x-1|+7sin(7x) continuous?

A: we have given function y=5x-1+7sin(7x) we know that  sin(ax) is continuous everywhere hence sin(7x)…

Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: Determine whether  the following statement is true or false, and explain why. If ƒ″(x) > 0 on an…

A: If the second derivative of a function f(x) is defined on an interval (a,b) and f ''(x) > 0 on…

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

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

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Q: What does it mean for a function to be left-continuous at a point?

A: function to be left-continuous at a point?

Q: Is the function given by f(x)=x^2+3x/2x-1 continuous over its domain?

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Q: What values must a and b take for f to be continuous everywhere?

A: Given that the function fx=ax1+4x2 ,      x<0b    ,                     x=0tan-1xx ,…

Q: Determine where the function f(x) is continuous. f(x) = /2-x

A: We have to determine where th function f(x)=(2-x)^(1/3) is continuous

Q: When can we say that a function is continuous at a number?

A: To explain: The continuity of a function at a point.

Q: f (x) = 2x² – x + 6 -

A: The given function,   f(x)=2x2-x+6

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

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Q: V16-x2 f(x) = at (-3,-1) x+1

A: Given function is fx=16-x2x+1 The interval is -3,-1 We know that function is continuous in any…

Q: f(x) = х-16 at (5,8) Vx-4

A: We have given function fx=x-16x-4 and point 5,8.

Q: Explain, using the theorems, why the function is continuous at every number in its domain. 2x² - x –…

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

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Q: find the value of c that make the function continuous

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Q: Which of the following functions are continuous? Why do you think they are continuous? hix fix

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Q: Is the following function continuous at a = 1? Explain why. x2 +4x 21 - f(x) = ifx # 3 X - 3 6. ifx…

A: Consider the function  fx=x2+4x−21x−3              x≠36                                 x=3

Q: Is the function continuous or discontinuous? If discontinuous, what condition is not satisfied?

A: Given:

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: At what points of R² are the following functions continuous?

A: A function is not continuous at the value of variables when the function does not give a defined…

Q: Which of the following does not represent a function that is continuous everywhere?

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Q: State the intervals on which the function f is continuous

A: A function is said to be in an interval if it's graph runs continuously without any break it that…

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

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Q: Adding two functions that are continuous everywhere yields a function that is continuous everywhere.…

A: given,         Adding two functions that are continuous everywhere yields a function that is…

Q: Describe the intervals on which the function is continuous.

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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.