All polynomial functions are continuous. * TRUE FALSE

Q: If the functions f and g are continuous for all real x, is f + g always continuous for all real x?…

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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: f(t) = 3 – 9 ? -6, [-3, 3]

A: To find: The continuity of the function f(t)=3-9-t2 on the interval [-3, 3]

Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: If the bound of error greater than zero, the polynomial is------than the .function not equal O its…

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Q: Describe the intervals on which the function is continuous. f(x) = −3x2 + 7

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Q: 2, if x -1 Find the value for a and b such that f (x) = {ax + b, if – 1 3 for all real numbers.

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous at x=-1 so we…

Q: Use Mean value theorem to show that (1+ x)' 2 (1+2x).x21.

A: Mean value theorem: Let f be a continuous function on the closed interval a, b and differentiable on…

Q: Write a delta - epsilon proof that shows that the function f(x) = 3x – 5 is continuous at æ = 2

A: Let ε>0 be given. Also let 0<δ<min1,ε3. Then for x-2<δ,…

Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

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Q: Determine the intervals on which the function is continuous. %3!

A: To find: The interval in which the function fx=12-x is continuous. Concept used: The domain of the…

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

A: to find: limx→-1x3+3

Q: Show that the functions are continuous on their natural domains with examples?

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Q: Exercise 2. Prove that all polynomials and rational functions are continuous on their domain.

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Q: Describe the intervals on which the function is continuous. f(x)= 4x2+7x-2 / x+2

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Q: function is continuous.

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Q: = Find a continuous function

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Q: Describe the intervals on which the function is continuous

A: fx=-3x2+7 It is a polynomial function of degree 2.

Q: Select all the intervals where g is decreasing.

A: Given data: The given graph of the curve g(x) is shown in the problem. By looking at the graph the…

Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1]

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Q: Find all intervals where the function f(x) = x+ x- x is increasing.

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Q: (a): Verify Mean value theorem for the function f(x) = 3x³ + x + 4 over the interval 0, 1].

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (a): Verify Mean value theorem for the function f(x) = 6x3 + x + 2 over the interval [0, 1].

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Q: Suppose that (picture) If f is  continuous for all real numbers, then c is equal to:

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Q: If function fis continuous on [-10,5], then which of the following statements must be true?

A: Remember : If a function is continuous on the [a,b] then it is differentiable on (a,b) and if it is…

Q: Evaluate f132 if lim f1x2 = 5, lim f1x2 = 6, and f is right- xS3* xS3- continuous at x = 3.

A: Known fact: A function f is said to be right continuous at a point a if limx→a+fx=fa.

Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: The principle of Analytic continuation:

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Q: Find all intervals where f is increasing.

A: Given,           f(x) =-x6x + 273

Q: Find continuous functions

A: Given,        fn:0, 1→[0, ∞)

Q: if f functions is bounded on [a,b] does f has an absolute maximum and absolute minimum or not??

A: if f functions is bounded on [a,b] does f has an absolute maximum and absolute minimum or not??

Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

Q: Prove that all functions can be written as a sum of an even function and an odd function

A: Show that: w(x)=u(x)+v(x) and also show that: u(x) is even and v(x) is odd,

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: 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: What is the sign-preserving property of continuous functions?

A: What is the sign-preserving property of continuous functions?

Q: Give an example of a sequence of continous functions on a compact domain converging pointwise but…

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Q: Determine whether the statement " If f is continuous for all x and y and has two relative minima,…

A: Given: If f is continuous for all x and y and has two relative minima, then f must have at least one…

Q: Determine whether the function shown is continuous over the interval (-5, 5).

A: We will determine whether the function is continuous over the interval (-5, 5) as following.

Q: Which . functions are continuous through its domain?

A: Continuous Function: A function fx is continuous at a point c of its domain if  limx→cfx=fc A…

Q: The graph of a polynomial function is always smooth andcontinuous. Name a function studied earlier…

A: The graph of a polynomial function is always smooth and continuous. Name a function studied earlier…

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

A: Continuous function: A function f(x) is continuous over an interval [a,b] if the function has no…

Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: DISCUSS THE CONTINUITY OF THE FUNCTION ON THE CLOSED INTERVAL

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Q: (a). Show that limit x→1, does not exist if (3-2х for x<1 f(x) = { 6x-4 for x21

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Q: Determine if the function is continuous. x4-1/x2-1

A: Given:     To determine: the function is continuous or not.

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: If a function is continuous on a closed interval, then the function will have an absolute maximum…

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Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…